Inclusion Criteria:

- PHASE I (REGISTRATION): Women must not be pregnant or breast-feeding; all females of
childbearing potential must have a blood test or urine study within 2 weeks prior to
registration to rule out pregnancy; a female of childbearing potential is any woman,
regardless of sexual orientation or whether they have undergone tubal ligation, who
meets the following criteria: 1) has not undergone a hysterectomy or bilateral
oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive
months (i.e., has had menses at any time in the preceding 24 consecutive months)

- PHASE I (REGISTRATION): Women of childbearing potential and sexually active males
must agree to use adequate contraception (hormonal or barrier method of birth
control; abstinence) prior to study entry and for the duration of study
participation; should a woman become pregnant or suspect she is pregnant while
participating in this study, she should inform her treating physician immediately

- PHASE I (REGISTRATION): Patients must have measurable or non-measureable disease
based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1; baseline
measurements and evaluations of all sites of disease must be obtained =< 4 weeks
prior to registration

- PHASE I (REGISTRATION): Patient must have histologically or pathologically confirmed
squamous NSCLC; patients whose tumors contain mixed NSCLC histologies are eligible if
squamous morphology is predominant; mixed tumors with small cell anaplastic elements
are not eligible

- PHASE I (REGISTRATION): Life expectancy >= 12 weeks

- PHASE I (REGISTRATION): Eastern Cooperative Oncology Group (ECOG) performance status
0 - 1

- PHASE I (REGISTRATION): Absolute neutrophil count >= 1,500/mcL

- PHASE I (REGISTRATION): Hemoglobin >= 9 g/dL

- PHASE I (REGISTRATION): Platelets >= 100,000/mcL

- PHASE I (REGISTRATION): Total bilirubin within normal institutional limits

- PHASE I (REGISTRATION): Corrected calcium within normal institutional limits;
corrected calcium is defined as ([4 - plasma albumin in g/dL] x 0.8 + serum calcium)

- PHASE I (REGISTRATION): Phosphate within normal institutional limits

- PHASE I (REGISTRATION): Aspartate aminotransferase (AST) (serum glutamic oxaloacetic
transaminase [SGOT]) and alanine aminotransferase (ALT) (serum glutamic pyruvate
transaminase [SGPT]) =< 3 x institutional upper limit of normal

- PHASE I (REGISTRATION): Creatinine clearance >= 55 mL/min (by actual, or estimated by
modified Cockcroft-Gault formula)

- PHASE I (REGISTRATION): Patients must have NONE of the following cardiac criteria:

- Mean resting corrected QT interval (QTc) < 470 msec obtained from 3 consecutive
electrocardiograms

- No clinically important abnormalities in rhythm, conduction or morphology of
resting electrocardiogram (ECG) e.g. complete left bundle branch block, third
degree heart block

- No factors that increase the risk of QTc prolongation or risk of arrhythmic
events such as heart failure, hypokalemia, congenital long QT syndrome, family
history of long QT syndrome or unexplained sudden death under 40 years of age or
any concomitant medication known to prolong the QT interval

- PHASE I (REGISTRATION): No prior treatment with docetaxel (except in the adjuvant
setting), or AZD4547

- PHASE I (REGISTRATION): No prior treatment with any other chemotherapy, immunotherapy
or anticancer agents within 2 weeks prior to registration

- PHASE I (REGISTRATION): Patient must have NONE of the following ophthalmological
conditions:

- Current evidence or previous history of retinal pigmented epithelium detachment
(RPED)

- Previous laser treatment or intra-ocular injection for treatment of macular
degeneration

- Current evidence or previous history of dry or wet age-related macular
degeneration

- Current evidence or previous history of retinal vein occlusion (RVO)

- Current evidence or previous history of retinal degenerative diseases (e.g.
hereditary)

- Current evidence or previous history of any other clinically relevant
chorioretinal defect

- PHASE I (REGISTRATION): No uncontrolled brain metastases; patients with brain
metastases must have stable neurologic status prior to registration for a minimum of
3 weeks after whole brain radiation or surgery, OR 1 week after stereotactic
radiosurgery for 3 or fewer lesions; patients must be without neurologic dysfunction
that would confound the evaluation of neurologic and other adverse events

- PHASE I (REGISTRATION): Patient must NOT have history of allergic reactions
attributed to compounds of similar chemical or biologic composition to AZD4547,
docetaxel or other agents used in the study

- PHASE I (REGISTRATION): No uncontrolled intercurrent illness including, but not
limited to, ongoing or active infection, symptomatic congestive heart failure,
unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social
situations that would limit compliance with study requirements

- PHASE I (REGISTRATION): Patient must NOT have refractory nausea and vomiting, chronic
gastrointestinal disease, inability to swallow the investigational drug, previous
significant bowel resection, or any other significant gastrointestinal disorder that
could, in the opinion of the Investigator, interfere with the absorption of AZD4547

- PHASE I (REGISTRATION): Patient must NOT have had a major surgical procedure within 3
weeks prior to registration

- PHASE I (REGISTRATION): Patient must NOT have >= grade 3 peripheral neuropathy, as
defined by the National Cancer Institute (NCI) Common Terminology Criteria for
Adverse Events (CTCAE),version 4.02

- PHASE I (REGISTRATION): Patient must NOT have known hepatitis B virus (HBV) or
hepatitis C virus (HCV) infection

- PHASE I (REGISTRATION): Patients with known human immunodeficiency virus (HIV) are
not eligible if cluster of differentiation (CD)4 count is =< 200 cell/mm^3 or if
receiving antiretroviral therapy due to potential unfavorable interactions of the
agents with the study treatment

- PHASE I (REGISTRATION): Patients may not be receiving any other investigational
agents while on study

- PHASE I (REGISTRATION): Patients should not be taking medications that are potent
inhibitors of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4),
cytochrome P450, family 2, subfamily C, polypeptide 8 (CYP2C8), cytochrome P450,
family 2, subfamily D, polypeptide 6 (CYP2D6), or substrates of CYP3A4 prior to the
first dose of study treatment

- PHASE II (PRE-REGISTRATION): Women must not be pregnant or breast feeding; all
females of childbearing potential must have a blood test or urine study within 2
weeks prior to registration to rule out pregnancy; a female of childbearing potential
is any woman, regardless of sexual orientation or whether they have undergone tubal
ligation, who meets the following criteria: 1) has not undergone a hysterectomy or
bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24
consecutive months (i.e., has had menses at any time in the preceding 24 consecutive
months) of childbearing potential and sexually active males must agree to use
adequate contraception (hormonal or barrier method of birth control; abstinence)

- PHASE II (PRE-REGISTRATION): Women of childbearing potential (defined as a
premenopausal female capable of becoming pregnant) and sexually active males must
agree to use adequate contraception (hormonal or barrier method of birth control;
abstinence) prior to study entry and for the duration of study participation; should
a woman become pregnant or suspect she is pregnant while participating in this study,
she should inform her treating physician immediately

- PHASE II (PRE-REGISTRATION): Patient must have histologically or pathologically
confirmed squamous NSCLC; patients whose tumors contain mixed NSCLC histologies are
eligible if squamous morphology is predominant; mixed tumors with small cell
anaplastic elements are not eligible

- PHASE II (PRE-REGISTRATION): Patient must have paraffin-embedded tumor specimen
available for submission for determination of fibroblast growth factor receptor
1(FGFR1) amplification status

- PHASE II (PRE-REGISTRATION): Life expectancy >= 12 weeks

- PHASE II (PRE-REGISTRATION): ECOG performance status 0 - 1

- PHASE II (PRE-REGISTRATION): Patient must have had one and only one prior systemic
therapy for metastatic disease or one prior systemic therapy for recurrent disease
after definitive local therapy

- PHASE II (PRE-REGISTRATION): No prior treatment with docetaxel (except in the
adjuvant setting), or AZD4547

- PHASE II (PRE-REGISTATION): Patient must NOT have history of allergic reactions
attributed to compounds of similar chemical or biologic composition to AZD4547,
docetaxel or other agents used in the study

- PHASE II (PRE-REGISTRATION): Patient must NOT have uncontrolled intercurrent illness
including, but not limited to, ongoing or active infection, symptomatic congestive
heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric
illness/social situations that would limit compliance with study requirements

- PHASE II (PRE-REGISTRATION): Patient must NOT have refractory nausea and vomiting,
chronic gastrointestinal disease, inability to swallow the investigational drug,
previous significant bowel resection, or any other significant gastrointestinal
disorder that could, in the opinion of the Investigator, interfere with the
absorption of AZD4547

- PHASE II (PRE-REGISTRATION): Patient must NOT have >= grade 3 peripheral neuropathy,
as defined by the NCI CTCAE, version 4.02

- PHASE II (PRE-REGISTRATION): Patient must NOT have known HBV or HCV infection

- PHASE II (PRE-REGISTRATION): Patients with known HIV are not eligible if CD4 count is
=< 200 cell/mm^3 or if receiving antiretroviral therapy due to potential unfavorable
interactions of the agents with the study treatment

- PHASE II (RANDOMIZATION): Patient must meet all eligibility criteria outlined in
pre-registration section

- PHASE II (RANDOMIZATION): Patient must have confirmed measurable disease based on
RECIST 1.1; baseline measurements and evaluations of all sites of disease must be
obtained =< 4 weeks prior to registration

- PHASE II (RANDOMIZATION): Women must not be pregnant or breast-feeding; all females
of childbearing potential must have a blood test or urine study within 2 weeks prior
to registration to rule out pregnancy; a female of childbearing potential is any
woman, regardless of sexual orientation or whether they have undergone tubal
ligation, who meets the following criteria: 1) has not undergone a hysterectomy or
bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24
consecutive months (i.e., has had menses at any time in the preceding 24 consecutive
months)

- PHASE II (RANDOMIZATION): Women of childbearing potential (defined as a premenopausal
female capable of becoming pregnant) and sexually active males must agree to use
adequate contraception (hormonal or barrier method of birth control; abstinence)
prior to study entry and for the duration of study participation; should a woman
become pregnant or suspect she is pregnant while participating in this study, she
should inform her treating physician immediately

- PHASE II (RADOMIZATION): Patient must have positive tumor FGFR1 gene amplification
(score fluorescence in situ hybridization [FISH]6) as determined by an AstraZeneca
approved central laboratory

- PHASE II (RANDOMIZATION): Life expectancy >= 12 weeks

- PHASE II (RAMDOMIZATION): ECOG performance status 0 - 1

- PHASE II (RANDOMIZATION): Absolute neutrophil count >= 1,500/mcL

- PHASE II (RANDOMIZATION): Platelets >= 100,000/mcL

- PHASE II (RANDOMIZATION): Total bilirubin within normal institutional limits

- PHASE II (RANDOMIZATION): Corrected calcium within normal institutional limits;
corrected calcium is defined as ([4 - plasma albumin in g/dL] x 0.8 + serum calcium

- PHASE II (RANDOMIZATION): Phosphate within normal institutional limits

- PHASE II (RANDOMIZATION): AST (SGOT) and ALT (SGPT) =< 3 x institutional upper limit
of normal

- PHASE II (RANDOMIZATION): Creatinine clearance >= 55 mL/min (actual, or estimated by
modified Cockcroft-Gault formula)

- PHASE II (RANDOMIZATION): Patients must have NONE of the following cardiac criteria:

- Mean resting QTc < 470 msec obtained from 3 consecutive electrocardiograms

- No clinically important abnormalities in rhythm, conduction or morphology of
resting ECG e.g. complete left bundle branch block, third degree heart block

- No factors that increase the risk of QTc prolongation or risk of arrhythmic
events such as heart failure, hypokalemia, congenital long QT syndrome, family
history of long QT syndrome or unexplained sudden death under 40 years of age or
any concomitant medication known to prolong the QT interval

- PHASE II (RANDOMIZATION): No prior treatment with any other chemotherapy,
immunotherapy or anticancer agents within 2 weeks prior to randomization

- PHASE II (RANDOMIZATION): Patient must have NONE of the following ophthalmological
conditions:

- Current evidence or previous history of RPED

- Previous laser treatment or intra-ocular injection for treatment of macular
degeneration

- Current evidence or previous history of dry or wet age-related macular
degeneration

- Current evidence or previous history of RVO

- Current evidence or previous history of retinal degenerative diseases (e.g.
hereditary)

- Current evidence or previous history of any other clinically relevant
chorioretinal defect

- PHASE II (RANDOMIZATION): Patient must have no uncontrolled brain metastases;
patients with brain metastases must have stable neurologic status prior to
registration for a minimum of 3 weeks after whole brain radiation or surgery, OR 1
week after stereotactic radiosurgery for 3 or fewer lesions; patients must be without
neurologic dysfunction that would confound the evaluation of neurologic and other
adverse events

- PHASE II (RANDOMIZATION): No major surgical procedure within 3 weeks prior to
randomization

- PHASE II (RANDOMIZATION): Patient must have no >= grade 3 peripheral neuropathy, as
defined by the NCI CTCAE, version 4.0

- PHASE II (RANDOMIZATION): Patients may not be receiving any other investigational
agents while on study

- PHASE II (REGISTRATION): Patient was randomized to docetaxel only (arm D) on step 1
and progressed per RECIST v1.1 criteria; registration to step 2 must occur within 4
weeks of confirmation/determination of disease progression

- PHASE II (REGISTRATION): Patient must have confirmed measurable disease based on
RECIST 1.1; baseline measurements and evaluations of all sites of disease must be
obtained =< 4 weeks prior to registration

- PHASE II (REGISTRATION): Women must not be pregnant or breast-feeding; all females of
childbearing potent