Inclusion Criteria:

- Patients must have a histologically or cytologically confirmed advanced or metastatic
solid tumor for which no standard curative measure exists (dose escalation) OR
patients must have histologically or cytologically documented locally advanced and
unresectable OR metastatic breast cancer (dose expansion)

- Patients must have either evaluable or measurable disease, defined as at least one
lesion that can be accurately measured in at least one dimension (longest diameter to
be recorded for non-nodal lesions and short axis for nodal lesions) as >= 20 mm with
conventional techniques or as >= 10 mm with spiral CT scan

- Patients must have HER2-positive (HER2+) cancer as defined by either: (a) 3+ for HER2
by immunohistochemistry (IHC), or (b) fluorescent in situ hybridization (FISH) or in
situ hybridization (ISH) mean locus-to-centromeric ratio greater than or equal to
2.2; these analyses must be determined on an invasive component of the cancer at
either the primary site or the metastatic site (dose expansion)

- Patients may have previously had disease progression on lapatinib, but should not
have demonstrated prior serious or life-threatening intolerance to doses of lapatinib
exceeding 1000 mg per day

- Life expectancy of greater than 12 weeks

- Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (or Karnofsky >=
60%)

- Leukocytes >= 3,000/mcL

- Absolute neutrophil count >= 1,500/mcL

- Platelets >= 100,000/mcL

- Total bilirubin =< upper limit of normal (ULN); in the case of a patient with known
Gilbert's disease, s/he will be eligible as long as total serum bilirubin is less
than 1.5 x ULN

- Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and
alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5
times upper limit of normal

- Creatinine =< ULN OR creatinine clearance >= 60 mL/min/1.73^2 by Cockcroft-Gault for
patients with creatinine levels above institutional normal

- Patients must have previously received trastuzumab, either in the adjuvant or
metastatic setting (dose expansion)

- Women of childbearing potential and men should use contraception (hormonal or barrier
method of birth control; abstinence) prior to study entry and for the duration of
study participation AS WELL AS for one month after stopping use of the study agents

- Should a woman become pregnant or suspect she is pregnant while she or her
partner is participating in this study, the patient should inform the treating
physician immediately

- All patients in this cohort must have archived primary or metastatic tissue blocks
available (dose expansion)

- Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

- Patients who have had chemotherapy, therapy with trastuzumab, bevacizumab or other
targeted therapy, or radiotherapy within 4 weeks (6 weeks for regimens including
carmustine [BCNU], nitrosoureas or mitomycin C) prior to entering the study; the
following will apply with regards to endocrine therapy:

- Patients receiving an aromatase inhibitor (AI) are eligible as long as they stop
the AI one day prior to beginning study agents

- Given the longer half-life, patients receiving tamoxifen or fulvestrant should
have received their last dose at least 2 weeks prior to beginning study agents

- Patients who have not recovered (=< grade 1) from adverse events due to agents
administered more than 4 weeks earlier (tolerable grade 2 adverse events may be
allowed at the discretion of the investigator)

- Patients may not be receiving any other investigational agents

- History of allergic reactions attributed to compounds of similar chemical or biologic
composition to MK-2206, lapatinib or other agents used in the study

- Patients receiving any medications or substances that are strong or moderate
inhibitors or inducers of CYP 450 3A4 are ineligible unless they can be transitioned
off this medication prior to study drug initiation

- Patients on strong or moderate inhibitors/inducers will become eligible if they
discontinue all such medications at least 5 days prior to start of therapy and
no further doses are anticipated for the duration of investigational therapy

- In order to be considered a contraindicated medication, a patient must be
taking the drug systemically and on a regular and scheduled basis; for
example, a topical medication taken intermittently need not be stopped

- Patients currently taking weak CYP3A4 inducers, and/or inhibitors are eligible

- Patients currently taking sensitive substrates with narrow therapeutic indices
are ineligible unless:

- The medication can be monitored clinically in the opinion of the principal
investigator (PI)/Study chair; monitoring will be performed on a schedule
to be determined by the PI/study chair and treating physician (MD); for
example, a substrate medication that can be clinically monitored is digoxin

- It the medication CANNOT be monitored clinically, they discontinue all such
medications at least 5 days prior to start of therapy and no further doses
are anticipated for the duration of investigational therapy

- Patients with diabetes or at risk for hyperglycemia should not be excluded from
trials with MK-2206, but the hyperglycemia should be well controlled before the
patient enters the trial

- Inadequately controlled diabetes mellitus or hyperglycemia will be defined as:

- Hemoglobin A1c > 8%

- Fasting blood glucose over 200

- Diabetes which requires injected insulin

- Patients with malabsorption syndrome or other condition that would interfere with
intestinal absorption; patients must be able to swallow tablets

- Preclinical studies indicated transient changes in QTc interval during MK-2206
treatment; prolongation of QTc interval is potentially a safety concern while on
MK-2206 therapy; a baseline QTcF > 450 msec (male) or QTcF > 470 msec (female) will
exclude patients from entry on study

- Congestive heart failure (CHF) is a known but rare complication of lapatinib;
therefore, patients with a left ventricular ejection function (LVEF) less than 50% or
the lower limit of institutional normal are ineligible

- 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

- Pregnant women are excluded from this study because MK-2206 and lapatinib are agents
with the potential for teratogenic or abortifacient effects; because there is an
unknown but potential risk for adverse events in nursing infants secondary to
treatment of the mother with these drugs, breastfeeding should be discontinued if the
mother is treated with either MK-2206 or lapatinib

- Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral
therapy are ineligible