Left ventricular ejection fraction (LVEF) >= institutional lower limit of normal (LLN) by echocardiogram (ECHO) or multigated acquisition scan (MUGA) within 30 days of day 1 of study Patients must have an echocardiogram (ECHO) or multigated acquisition (MUGA) scan within 42 days prior to registration with a cardiac ejection fraction >= 45% Left ventricular ejection fraction >= 50%, as determined by multigated acquisition (MUGA) or echocardiogram within 30 days prior to protocol registration Patients must have left ventricular ejection fraction (LVEF) >= 50 as measured by echocardiogram or multigated acquisition scan (MUGA) Patients with an ejection fraction < 50% assessed by multigated acquisition scan (MUGA) or echocardiogram (ECHO) scan within 7 days of day 1 Left ventricular ejection fraction (LVEF) must be within institutional limits of normal as assessed by echocardiogram or multigated acquisition scan (MUGA) documented within 28 days prior to first dose of study drug Participants with a history of chronic heart failure or significant cardiovascular disease must have an echocardiogram or multigated acquisition scan indicating left ventricular ejection fraction greater than or equal to 45% within 28 days prior to the first dose of study drug. Left ventricular ejection fraction (LVEF) >= 50% by 2-dimensional (2D) echocardiogram (ECHO) or multigated acquisition (MUGA) scan; timeline: within 4 weeks prior to enrollment Left ventricular ejection fraction; LVEF >= 40% (by echocardiogram or multigated acquisition scan [MUGA] testing) For Part F (LY2835219 + trastuzumab):The participant must have received at least 1 chemotherapy regimen for metastatic disease and may be receiving ongoing therapy with trastuzumab. The participant must have an estimated left ventricular ejection fraction within the normal range by either echocardiogram or multigated acquisition (MUGA) scan Patients with symptomatic left ventricular dysfunction or baseline left ventricular ejection fraction (LVEF) my multigated acquisition scan (MUGA) or echocardiogram (ECHO) of =< 50% are not eligible Left ventricular ejection fraction (LVEF) >= 50% (determined by echocardiogram or multigated acquisition scan) within 42 days of treatment Left ventricular ejection fraction (LVEF) ? 50% by echocardiogram (echo) or multigated acquisition (MUGA) scan within 28 days before day 1 of study Have a left ventricular ejection fraction (LVEF) >45% by echocardiogram (ECHO) or multigated acquisition (MUGA) scan On echocardiogram, documented left ventricular ejection fraction > 45%; patients may instead have a multigated acquisition (MUGA) scan instead of transthoracic echocardiogram (TTE). ENROLLMENT TO THE DOSE ESCALATION, EXPANSION AND PART II: Left ventricular ejection fraction (LVEF) >= 50% as determined by echocardiogram or multigated acquisition scan (MUGA) Left ventricular cardiac ejection fraction of ?45% by echocardiogram or multigated acquisition (MUGA) scan Left ventricular ejection fraction >= 45% by multigated acquisition scan (MUGA) or echocardiogram Left ventricular ejection fraction >= 40% by 2 dimensional (D) echocardiogram (ECHO) or multigated acquisition (MUGA) scan, or left ventricular shortening fraction >= 20% by ECHO for patients receiving MAC, RIC or RIC-MMF, or LVEF > 30%; if the patient has radiologic evidence of aortic, renal, or coronary artery vasculitis, LVEF >= 30% for patients receiving IOC Left ventricular ejection fraction (LVEF) must be equal to or greater than 50%, as measured by multigated acquisition (MUGA) scan or echocardiogram Ejection fraction measured by echocardiogram or multigated acquisition (MUGA) >= 50% Baseline multigated acquisition scan (MUGA) or echocardiogram (ECHO) done only in subjects with prior doxorubicin exposure. The test must demonstrate left ventricular ejection fraction (LVEF) >= the lower limit of the institutional normal Left ventricular ejection fraction (LVEF) >= lower limit of normal (LLN) as assessed by either multigated acquisition (MUGA) scan or echocardiogram (ECHO) Have current or a history of congestive heart failure New York Heart Association (NYHA) class 3 or 4, or any history of documented diastolic or systolic dysfunction (left ventricular ejection fraction [LVEF] < 40%, as measured by multigated acquisition [MUGA] scan or echocardiogram) Ejection fraction < 50% on screening echocardiography (ECHO) or multigated acquisition scan (MUGA). Cardiac ejection fraction within institutional normal limits by either multigated acquisition scan (MUGA) or echocardiogram (ECHO) at baseline If the participant is to be enrolled in the doxorubicin combination arm, a left ventricular dysfunction (LVEF < 50%) or shortening fraction of <27% by echocardiogram (either multigated acquisition [MUGA] or echocardiogram [ECHO] are required, not both). Must be hemodynamically stable at the time of ET190L1-ARTEMIS T cell administration and have left ventricular ejection fraction (LVEF) ? 45% confirmed by echocardiogram or multigated acquisition scan (MUGA) scan Within 4 weeks before enrollment: Left ventricular ejection fraction (LVEF) > 45% by multigated acquisition (MUGA) or rest echocardiogram (ECHO) Adequate cardiac function, defined as left ventricular ejection fraction (LVEF) of >= 50% as assessed by echocardiogram or multigated acquisition (MUGA) scan, or LVEF of 45-49% and clearance by a cardiologist Left ventricular ejection fraction (LVEF) ? 55% at rest (multigated acquisition [MUGA] scan or echocardiogram [Echo]) Left ventricular ejection fraction greater than (>) 50% as measured by ECHO or MUGA scan within 4 weeks before receiving the first dose of study drug. Has left ventricular ejection fraction (LVEF) < 45% by either echocardiogram (ECHO) or multigated acquisition (MUGA) scan. Left ventricular ejection fraction (LVEF) >= lower limit of normal (LLN) by echocardiography (ECHO) or multigated acquisition (MUGA) Cardiac echocardiogram, stress test, or multigated acquisition (MUGA) within past 6 months with demonstrated left ventricular ejection fraction (LVEF) > 50% Left ventricular ejection fraction >= 50% measured by multigated acquisition (MUGA) scan or echocardiogram If a patient has received anthracycline chemotherapy after prior enrollment on PLAT-02, they must have an echocardiogram to demonstrate shortening fraction > 28% or multigated acquisition scan (MUGA) to demonstrate ejection fraction of > 50%; the echocardiogram or MUGA can be done at any time following the anthracycline (does NOT need to be within 48 hours of the T cell infusion) (For cohort B): Baseline multigated acquisition (MUGA) or echocardiogram showing left ventricular ejection fraction (LVEF) >= 50% within 6 weeks prior to initiation of NACT Left ventricular ejection fraction (LVEF) >= lower limit of normal (LLN) by echocardiogram (ECHO) or multigated acquisition scan (MUGA) Impaired cardiac function (left ventricular ejection fraction [LVEF] < 40%) as assessed by echocardiogram (ECHO) or multigated acquisition (MUGA) scan Left ventricular ejection fraction (LVEF) >= 50% by transthoracic echocardiogram or multigated acquisition scan (MUGA) Patients have left ventricular ejection fraction (LVEF) >= 50% by multigated acquisition scan (MUGA) or echocardiogram before study randomization Baseline left ventricular ejection fraction of at least 40% by multigated acquisition (MUGA) or echocardiography (ECHO) Left ventricular ejection fraction (LVEF) at rest >= 40%; for patients aged < 13 years, shortening fraction (SF) >= 26% by echocardiogram or LVEF by multigated acquisition scan (MUGA) may be used Left ventricular ejection fraction (LVEF) < 50% as determined by multigated acquisition (MUGA) scan or electrocardiogram (ECHO), or uncontrolled hypertension (refer to World Health Organization-International Society of Hypertension [WHO-ISH] guidelines) Adequate cardiac function as defined by the following:\r\n* Left ventricular ejection fraction (LVEF) >= 50% as determined by a multigated acquisition (MUGA) scan or echocardiogram\r\n* Corrected QT interval (QTc) interval =< 480 ms (preferably the mean from triplicate electrocardiogram [ECG’s]) Left ventricular ejection fraction (LVEF) lower limit of normal (LLN) as assessed by either multigated acquisition (MUGA) scan or echocardiogram (ECHO) Left ventricular ejection fraction (LVEF) >= institutional lower limit of normal (LLN) by echocardiogram (ECHO) or multigated acquisition scan (MUGA) Ejection fraction of > 40% by multigated acquisition (MUGA) or echocardiogram Ejection fraction measured by echocardiogram or multigated acquisition scan (MUGA) >= 50% Cardiac ejection fraction >= 40% (by either echocardiogram [ECHO] or multigated acquisition [MUGA]) If prior history of ischemic heart disease or exposure to 200 mg/m^2 of doxorubicin, patients must have a measured ejection fraction (either by multigated acquisition scan [MUGA], echocardiogram [ECHO], stress test, or ventriculography) of at least 45% Shortening fraction > 28% by echocardiogram or an ejection fraction > 50% by multigated acquisition scan (MUGA) Cardiac ejection fraction > 50% (for HER2+ patients) as assessed by echocardiogram, multigated acquisition (MUGA) scan, or cardiac magnetic resonance imaging (MRI) Left ventricular ejection fraction (LVEF) of 50% or above, by multigated acquisition scan (MUGA) or echocardiogram If the research participant is to undergo leukapheresis, he/she must have ejection fraction measured by echocardiogram or multigated acquisition scan (MUGA) > 45% (within 6 weeks of time of screening) Ejection fraction >=40% by transthoracic echocardiogram or radionuclide ventriculogram, i.e. multigated acquisition (MUGA) scan Left ventricular ejection fraction (LVEF) greater than or equal to 50% as determined by a multigated acquisition (MUGA) scan or echocardiogram (Phase II only) Patients must have adequate cardiac function (left ventricular ejection fraction [LVEF]) >= 50% as determined by a multigated acquisition (MUGA) scan or echocardiogram Left ventricular ejection fraction (EF) > 40% by echocardiogram, multigated acquisition scan (MUGA), or cardiac magnetic resonance (MR) Left ventricular ejection fraction (LVEF) >= 40% as assessed by echocardiogram (ECHO) or multigated acquisition (MUGA) or other similar cardia imaging performed within 1 month of treatment Have a left ventricular ejection fraction (LVEF) >45% by echocardiogram (ECHO) or multigated acquisition (MUGA) scan Patients with a cardiac ejection fraction (as measured by either multigated acquisition scan [MUGA] or echocardiogram) < 40% are excluded Left ventricular ejection fraction (LVEF) assessment must be performed within 6 weeks prior to randomization; (LVEF assessment performed by echocardiogram is preferred; however, multigated acquisition scan (MUGA) scan may be substituted based on institutional preferences); the LVEF must be >= 55% regardless of the cardiac imaging facility's lower limit of normal Left ventricular ejection fraction (LVEF) >= 50% measured by multigated acquisition (MUGA) scan, echo, or stress test study with myocardial perfusion imaging Left ventricular ejection fraction (LVEF) >= 45% as determined by a multigated acquisition (MUGA) scan or echocardiogram, and QTc interval =< 480ms Left ventricular ejection fraction (LVEF) >= lower limit of normal (LLN) by echocardiogram (ECHO) or multigated acquisition (MUGA) To be performed within 28 days prior to day 1 of protocol therapy: Left ventricular ejection fraction >= 50% as determined by multigated acquisition (MUGA) scan or echocardiogram Left ventricular ejection fraction (LVEF) >= 50% calculated by echocardiogram (ECHO) or multigated acquisition scan (MUGA) Ejection fraction (EF) >= 50% by multigated acquisition (MUGA) or echocardiography (ECHO) within 4 weeks prior to first dose of study treatment Adequate cardiac function:\r\n* Left ventricular ejection fraction (LVEF) >= 50% as determined by multigated acquisition (MUGA) scan or echocardiogram (echo)\r\n* Corrected QT (QTc) interval =< 480 ms Left ventricular ejection fraction (LVEF) >= 45% at rest (multigated acquisition scan [MUGA] or echocardiogram [Echo]) Patients must have multigated acquisition (MUGA)/echocardiogram performed within 28 days prior to sub-study registration Ejection fraction (EF) measured by two-dimensional echocardiogram (2D-ECHO) or multigated acquisition scan (MUGA) scan of >= 45% Baseline multigated acquisition scan (MUGA) or echocardiogram (ECHO) must demonstrate left ventricular ejection fraction (LVEF) >= 45% Left ventricular ejection fraction (LVEF) >= 50% by echocardiogram (ECHO) or multigated acquisition scan (MUGA); same method as used at baseline must be use throughout the study, ECHO is the preferred method Left ventricular ejection fraction (LVEF) by echocardiogram (ECHO) or multigated acquisition (MUGA) > 40% Left ventricular ejection fraction >= 45% by multigated acquisition scan (MUGA) or echocardiogram (ECHO), fractional shortening >= 28% by ECHO Left ventricular ejection fraction at or above institutional lower limit of normal (obtained within 8 weeks of registration by multigated acquisition [MUGA] scan or echocardiogram; the same test performed at baseline should be repeated after every 3 cycles of therapy) Cardiac ejection fraction at or above the lower limit of normal as measured by multigated radionuclide angiography (MUGA) scans or echocardiogram documented =< 3 months prior to registration Patients must have a left ventricular ejection fraction >= lower limit of normal by echocardiogram (ECHO) or multigated acquisition scan (MUGA) Have left ventricular ejection fraction by multigated acquisition scan (MUGA) scan or 2D-ECHO within normal limits for the institution Patients with a known history of congestive heart failure or cardiac ejection fraction < 50% (or less than institutional normal limits); echocardiogram (ECHO) or multigated acquisition scan (MUGA) is not required prior to enrollment; for patients assigned to the chemotherapy arm, an ECHO or MUGA should be done within 6 months of day 1 of gemcitabine-docetaxel treatment\r\n* Patients who enroll on study and are randomized to Regimen I (chemotherapy ) and then are found on baseline ECHO or MUGA to have cardiac ejection fraction < 50% or below institutional normal will remain ON study; such patients will receive gemcitabine + docetaxel for 4 cycles but will NOT receive any doxorubicin treatment; they will continue treatment follow-up as outlined for all patients assigned to Regimen I Left ventricular ejection fraction >= lower limit of normal as assessed by echocardiogram or multigated acquisition scan Patients who received prior therapy with anthracyclines should have a baseline multigated acquisition scan (MUGA) or echocardiogram (echo) with a normal ejection fraction within 28 days prior to randomization left ventricular ejection fraction (LVEF) < 45% as determined by multigated acquisition (MUGA) scan or echocardiography (ECHO). Patients must have a left ventricular ejection fraction (LVEF) >= 50% by (either multigated acquisition [MUGA] or 2-dimensional [2-D] echocardiogram) within 28 days of registration Left ventricular ejection fraction (LVEF) >= 40% as confirmed by echocardiogram (ECHO)/multigated acquisition (MUGA) Patient must have adequate cardiac function (left ventricular ejection fraction [LVEF] >= 50% as determined by a multigated acquisition [MUGA] scan or echocardiogram; and corrected QT [QTc] interval =< 480 ms by Fridericia’s formula [QTcF]) Cardiac left ventricular function with resting ejection fraction >50% as determined by echocardiogram (ECHO) or multigated acquisition scan (MUGA). Patients older than 70 years of age should have left ventricular ejection fraction within ULN by multigated acquisition (MUGA) or 2-dimensional (2D) echocardiogram Left ventricular ejection fraction (LVEF) < 50% as determined by a multigated acquisition (MUGA) scan or echocardiogram Left ventricular ejection fraction (LVEF) defined by multigated acquisition (MUGA) or echocardiogram which is below the institutional lower limit of normal prior to starting study treatment Has a left ventricular ejection fraction (LVEF) within the normal institutional range (or >= 50%) based on an echocardiogram (ECHO) or multigated acquisition scan (MUGA), completed within 4 weeks prior to day one of treatment Baseline Left ventricular ejection fraction (LVEF) >=50% as measured by Echocardiogram (ECHO) or Multigated acquisition (MUGA) and above the testing institution's lower limit of normal Left ventricular ejection fraction (LVEF) >= 40% on 2-dimentional (2-D) transthoracic echocardiogram (ECHO); multigated acquisition scan (MUGA) is acceptable Adequate cardiac function defined as left ventricular ejection fraction (LVEF) >= 40%\r\n* NOTE: 2-dimensional (2-D) transthoracic echocardiogram (ECHO) is the preferred method of evaluation\r\n* Multigated acquisition scan (MUGA) is acceptable if ECHO is not available Left ventricular ejection fraction (LVEF) must be within institutional limits of normal as assessed by echocardiogram or multigated acquisition scan (MUGA) documented within 4 weeks prior to first dose of study drug. Left ventricular ejection fraction (LVEF) >= institutional lower limit of normal (LLN) by echocardiogram (ECHO) or multigated acquisition scan (MUGA) Have a 12-lead electrocardiogram (ECG) and echocardiogram (ECHO) or multigated acquisition (MUGA) scan performed by the investigator or other qualified person to evaluate cardiac function prior to enrollment in the study Left ventricular ejection fraction >= 50%, as determined by radionuclide ventriculogram (RVG) (multigated acquisition [MUGA]) or echocardiogram (ECHO) within 60 days prior to initiation of protocol therapy Patient must have a left ventricular ejection fraction >= institutional lower limit of normal (LLN) by echocardiogram (ECHO) or multigated acquisition (MUGA) within 28 days prior to registration Normal left ventricular ejection fraction on multigated acquisition scan (MUGA) or echocardiogram within the past 1 year prior to registration for patients with history of congestive heart failure and/or coronary disease requiring medications other than aspirin, or known prior exposure to anthracycline chemotherapy Ejection fraction by echocardiogram (ECHO) or multigated acquisition scan (MUGA) of >= 40% performed Adequate cardiac function (left ventricular ejection fraction [LVEF] > 40%) as assessed by echocardiogram (ECHO) or multigated acquisition (MUGA) scan performed within 1 month of treatment Ejection fraction >= 45% as determined by transthoracic echocardiogram or multigated acquisition scan (MUGA) Cardiac ejection fraction >= lower limit of normal as determined by 2-dimensional (D) echocardiogram (echo) or multigated acquisition (MUGA) scan according to institutional standards Cardiac ejection fraction, as assessed by either multigated acquisition (MUGA) scan or echocardiogram, greater than or equal to 50%, within 28 days prior to registration Left ventricle ejection fraction (LVEF) >= 40%; 2-dimensional (D) transthoracic echocardiogram (ECHO) is the preferred method of evaluation; multigated acquisition scan (MUGA) is acceptable if ECHO is not available Left ventricular ejection fraction >= the lower limit of normal by echocardiogram (ECHO) or multigated acquisition scan (MUGA) Left ventricular ejection fraction > 45% by either multigated acquisition scan (MUGA) or 2-dimensional (2-D) echocardiogram (echo), obtained within 28 days of enrollment; patients who have a prior cumulative anthracycline dose greater than 450 mg/m^2 will also have a cardiology consult to determine if further anthracycline administration is an absolute contraindication in patients who may require induction chemotherapy with EPOCH-F Ejection fraction (EF) of at least >= 40% by multigated acquisition (MUGA) or echocardiography (ECHO) Left ventricular ejection fraction (LVEF) within institutional range of normal as measured by echocardiogram (ECHO); multigated acquisition (MUGA) scans will be accepted in cases where an echocardiogram cannot be performed or is inconclusive (LVEF of > 50% required if normal range LVEF is not provided by institution) Baseline (< 1 month before treatment) cardiac left ventricular function with resting ejection fraction of less than 50% measured by multigated blood pool imaging of the heart (MUGA scan) or echocardiogram Left ventricular ejection fraction (LVEF) >= 50% as determined by a multigated acquisition (MUGA) scan or echocardiogram Left ventricular ejection fraction by multigated acquisition scan (MUGA) or echocardiogram >= 55% for patients with triple negative breast cancer; >= upper limit of institutional normal for patient with HR+ breast cancer within 7 days of treatment initiation Left ventricular ejection fraction =< 50% as demonstrated by echocardiogram or multigated acquisition scan (MUGA) Patients with left ventricular ejection fraction < 50% on echocardiogram or multigated acquisition scan will be excluded Baseline multigated acquisition scan (MUGA) or echocardiogram (ECHO) must demonstrate left ventricular ejection fraction (LVEF) >= 50% Cardiac ejection fraction >= 40% (by either cardiac echocardiogram [echo] or multigated acquisition [MUGA] scan); documentation of recent (=< 6 months from screening) outside reports is acceptable Adequate organ function defined by the screening laboratory inclusion listed below and Left Ventricular Ejection Fraction (LVEF) ? 45% confirmed by ECHO or multigated acquisition (MUGA) Left ventricular ejection fraction (LVEF) >= 40% (multigated acquisition scan [MUGA] or echocardiogram) All patients must have an echo or multigated acquisition (MUGA) scan showing ejection fraction (EF) > 50% and normal troponin and creatine kinase MB (CK MB) performed within 90 days of starting treatment Cardiac ejection fraction >= 50%, as measured by echocardiography (ECHO) or multigated acquisition scan (MUGA) Left ventricular ejection fraction (LVEF) >= 50% as determined by a multigated acquisition (MUGA) scan or echocardiogram Left ventricular ejection fraction >= institutional lower limit of normal (LLN) by echocardiogram (ECHO) or multigated acquisition scan (MUGA) Symptomatic left ventricular dysfunction or baseline left ventricular ejection fraction (LVEF) by multigated acquisition scan (MUGA) or echocardiogram (ECHO) =< 50% lower limit of institutional normal (LLN) Left ventricular ejection fraction (LVEF) > 40% (by echocardiogram [ECHO] or multigated acquisition scan [MUGA]) Left ventricular ejection fraction (LVEF) >= 50% by either echocardiogram (ECHO) or multigated acquisition scan (MUGA) Left ventricular ejection fraction (LVEF) >= 40% within 30 days before cycle 1 day 1; 2-dimensional (2-D) transthoracic echocardiogram (ECHO) is the preferred method of evaluation; multigated acquisition (MUGA) is acceptable if ECHO is not available Patients must have a pre-study echocardiogram or multigated acquisition (MUGA) scan with an actual left ventricular ejection fraction of greater than or equal to the institution lower limit of normal within one month prior to start of study. Left ventricular ejection fraction (LVEF) ?institutional lower limit of normal as measured by multigated acquisition scan (MUGA) or 2-dimensional (2-D) echocardiography (ECHO) within 28 days prior to start of therapy and no clinically significant abnormalities on a 12-lead electrocardiogram (ECG) All patients must have an left ventricular ejection fraction (LVEF) measurement of at least 50% by echocardiogram (ECHO) or multigated acquisition scan (MUGA) (if clinically indicated) within 14 days prior to registration; the method used for LVEF assessment in an individual subject must be the same throughout the trial Left ventricular ejection fraction > 50% on echocardiography or multigated acquisition (ECHO/MUGA) scan Left ventricular ejection fraction (LVEF) >= 50% as determined by a multigated acquisition (MUGA) scan or echocardiogram (ECHO) Uncontrolled or severe cardiovascular disease or left ventricular ejection fraction < 50% as determined by echocardiogram or multigated acquisition scan (MUGA) A resting ejection fraction of 50% or greater which increases with exercise as demonstrated by resting/exercise multigated acquisition (MUGA) or ejection fraction of 50% or greater by echocardiogram Left ventricular ejection fraction (LVEF) greater or equal to 50% at baseline as determined by either echocardiogram (ECHO) or multigated acquisition (MUGA) Left ventricular ejection fraction (LVEF) >= 50% by multigated acquisition scan (MUGA) scan or echocardiogram (ECHO) Left ventricular ejection fraction (LVEF) >= 45% by multigated acquisition (MUGA) scan or echocardiogram Subject has left ventricular ejection fraction (LVEF) ? 50%, or below institution's lower limit of normal (whichever is lower) by echocardiogram (ECHO) or multigated acquisition (MUGA) scan. Have current or a history of congestive heart failure New York Heart Association (NYHA) class 3 or 4, or any history of documented diastolic or systolic dysfunction (left ventricular ejection fraction [LVEF] < 40%, as measured by multigated acquisition [MUGA] scan or echocardiogram) Has left ventricular ejection fraction (LVEF) < 45% by either echocardiogram (ECHO) or multigated acquisition scan (MUGA)