Any prior cumulative doxorubicin dose must be ? 360 mg/m2; prior cumulative epirubicin dose must be ? 720 mg/m2. History of exposure to certain cumulative doses of anthracyclines History of exposure to cumulative doxorubicin dose ? 360 mg/meter squared. If another anthracycline or more than one anthracycline has been used, then the cumulative dose must not exceed the equivalent of 360 mg/meter squared of doxorubicin Greater than 5 weeks from doxorubicin at the time of consent, with radiation to be initiated no less than 6 weeks from doxorubicin Cumulative dose of doxorubicin or equivalent of > 360 mg/m^2 during prior adjuvant therapy Received previous systemic chemotherapy with a cumulative dose of > 900 mg/m^2 of epirubicin or > 400 mg/m^2 of doxorubicin If liposomal doxorubicin hydrochloride (DOXIL) is selected as the investigator’s choice chemotherapy:\r\n* Lifetime exposure to doxorubicin =< 240 mg/m^2 (or equivalent biologic dose if prior exposure to a different anthracycline) Cumulative anthracycline exposure greater than 450mg/m^2 doxorubicin equivalents prior to enrollment Cumulative doxorubicin dose >= 400 mg/m^2 (> 450 mg/m^2 for malignant soft tissue and bone tumor patients) or cumulative epirubicin dose >= 800 mg/m^2 Cumulative anthracyclines must not exceed 450 mg/m^2 doxorubicin equivalents following completion of treatment on protocol; therefore for patients receiving one course on protocol cumulative anthracyclines must be less than or equal to 400 mg/m^2 doxorubicin equivalents at the time of enrollment Prior anthracycline cumulative dose below 550 mg/m2 or the daunorubicin equivalent which is the recommended non-cardiotoxic level. Patients with a prior cumulative cisplatin dose > 300 mg/m^2 (pertains to Arm A only) Patients have received a cumulative dose of doxorubicin of greater than 360 mg/m^2 or epirubicin of greater than 640 mg/m^2 Patients who have received a cumulative doxorubicin equivalent of > 375 mg/m^2 total lifetime dose Prior therapy resulting in cumulative epirubicin dose >= 900 mg/m^2 or cumulative doxorubicin dose >= 500mg/m^2 or equivalent dose of another anthracycline Patients who have received a cumulative dose of doxorubicin of greater than 360 mg/m^2 or epirubicin of greater than 640 mg/m^2 Planning to initiate treatment with doxorubicin (starting dose of 75 mg/m^2) and olaratumab (starting dose of 15 mg/kg) as routine care Cumulative lifetime anthracycline dose of =< 450mg/m^2 Prior cumulative dose of doxorubicin of greater than 360 mg/m^2 or epirubicin of greater than 640 mg/m^2 Prior anthracycline therapy does not exceed 200 mg/m^2 total cumulative dose Previous treatment with complete cumulative doses of daunorubicin, idarubicin, and/or other anthracyclines and anthracenediones that is equivalent to a total dose of > 200 mg/m^2 doxorubicin If history of exposure to anthracyclines during perioperative treatment, the following cumulative doses of anthracyclines must be less than:\r\n* Epirubicin < 720 mg/m^2\r\n* Doxorubicin or liposomal doxorubicin < 360 mg/m^2\r\n* Mitoxantrone > 120 mg/m^2 and idarubicin > 90 mg/m^2\r\nIf more than one anthracycline has been used, then the cumulative dose must not exceed the equivalent of 360 mg/m^2 of doxorubicin Prior exposure to >375 mg/m2 of doxorubicin or liposomal doxorubicin. History of exposure to cumulative doses of doxorubicin greater than 360 mg per square meter of body-surface area or its equivalent Patients with treatment related myeloid neoplasms with cumulative anthracyclines greater than 230 mg/m^2 doxorubicin equivalents Patients who have received > 450 mg/m^2 daunorubicin equivalents; patients who relapse after receiving AAML0531/AAML1031 therapy will be eligible for this study, provided they have not received any additional anthracyclines; NOTE: for the purposes of determining eligibility for this protocol, the following cardiotoxicity multipliers will be used to determine daunorubicin equivalents:\r\n* Doxorubicin (doxorubicin hydrochloride): 1\r\n* Mitoxantrone: 3\r\n* Idarubicin: 3\r\n* Epirubicin: 0.5 No more than a total cumulative dose of 450 mg/m^2 of prior doxorubicin chemotherapy Cumulative lifetime dose of anthracycline chemotherapeutic > 80 mg/m^2 Patients who have received prior doxorubicin may not have had more than 320 mg/m^2 total dose and must have a normal left ventricular ejection fraction (LVEF) (>= 45%); (this includes Doxil or other liposomally encapsulated doxorubicin preparations) The participant received previous chemotherapy with a cumulative dose of >900 mg per meter squared (mg/m^2) of epirubicin or >400 mg/m^2 of doxorubicin. Prior treatment with anthracyclines at cumulative doses of 450 mg/m² or more for doxorubicin or 900 mg/m² or more for epirubicin Prior exposure to cumulative doses of doxorubicin >400 mg/m2 or epirubicin >720 mg/m2 Prior treatment with doxorubicin or other anthracycline at cumulative doses greater than 300 mg/m2 (calculated using doxorubicin equivalent doses: 1 mg doxorubicin = 1 mg Doxil/Caelyx = 1.8 mg epirubicin = 0.3 mg mitoxantrone = 0.25 mg idarubicin) History of exposure to the cumulative doses of anthracyclines History of prior cumulative exposure to >= 300 mg/m^2 cisplatin, area under the curve (AUC) of 18 of carboplatin, or their combined equivalent within one year prior to enrollment Subject has received a cumulative anthracycline dose above 400 mg/m2 of doxorubicin (or cumulative maximum dose of another anthracycline). History of exposure at any time to the following cumulative doses of anthracyclines:\r\n* Doxorubicin or liposomal doxorubicin > 500 mg/m^2\r\n* Epirubicin > 900 mg/m^2\r\n* Mitoxantrone >120 mg/m^2\r\n* Another anthracycline, or more than one anthracycline used in a cumulative dose exceeding the equivalent of doxorubicin 500 mg/m^2 Prior cumulative exposure to doxorubicin (including liposomal preparation) > 350 mg/m^2 Patients with therapy-related AML or MDS should have not received prior cumulative anthracycline (daunorubicin equivalent) lifetime dose > 450 mg/m^2 Patients who have previously had > 368 mg/m^2 cumulative dose of daunorubicin or > 368 mg/m^2 daunorubicin-equivalent anthracycline therapy (for example, from prior treatment of solid tumors) Patient had prior exposure to a cumulative dose of doxorubicin that exceeded 360 mg/m2 or its equivalent. Received prior therapy resulting in a cumulative epirubicin dose > 900 mg/m^2 or cumulative doxorubicin dose > 450 mg/m^2; if another anthracycline or more than one anthracycline has been used, the cumulative dose must not exceed the equivalent of 450 mg/m^2 doxorubicin Previous treatment with complete cumulative doses of daunorubicin, idarubicin, and/or other anthracyclines and anthracenediones that is equivalent to a total dose of 240 mg/m^2 doxorubicin Prior exposure to systemic intravenously given doxorubicin Prior treatment with doxorubicin (doxorubicin hydrochloride) up to 400 mg/m^2 History of exposure to the following cumulative doses of anthracyclines: Doxorubicin > 240 mg/m2; Epirubicin or Liposomal Doxorubicin-Hydrochloride (Myocet®) > 480 mg/m2; For other anthracyclines, exposure equivalent to doxorubicin > 240 mg/m2 Patients with prior cumulative anthracycline exposure of greater than 368 mg/m2 daunorubicin (or equivalent). Maximum prior cumulative doxorubicin dose of =< 360 mg/m^2 or equivalent Cumulative anthracycline exposure greater than 200 mg/m^2 doxorubicin isotoxic equivalents Prior treatment with cumulative dose of doxorubicin or equivalent exceeding 450 mg/m2 History of cumulative doxorubicin or liposomal doxorubicin dose > 430 mg/m^2 Prior treatment with anthracyclines with a cumulative dose of doxorubicin of greater than 400 mg/m2, or of epirubicin dose of greater than 800 mg/m2, or the equivalent dose for other anthracyclines or derivatives (part 2 only). No more than 3 prior lines of chemotherapy; prior therapy with doxorubicin is permitted but no more than lifetime cumulative dose of 150 mg/m^2; at least 3 weeks since prior chemotherapy or radiotherapy, at least 6 weeks if the last regimen included bis-chloroethylnitrosourea (BCNU) or mitomycin C Patients who have previously been treated with doxorubicin, liposomal doxorubicin, epirubicin, mitoxantrone, or any other anthracycline derivative Prior anthracycline therapy with a cumulative dose of doxorubicin (or equivalent) >= 400 mg/m^2 Prior exposure to anthracyclines or anthracenediones including doxorubicin, daunorubicin, and mitoxantrone Any prior cumulative doxorubicin dose must be ? 360 mg/m2; prior cumulative epirubicin dose must be ? 720 mg/m2. Prior exposure to greater than 360 mg/m2 doxorubicin or liposomal doxorubicin, greater than 120 mg/m2 mitoxantrone, greater than 90 mg/m2 idarubicin, or greater than 720 mg/m2 epirubicin History of exposure to the following cumulative doses of anthracyclines: Doxorubicin or liposomal doxorubicin >350 mg/m². Epirubicin >530 mg/m². If another anthracycline or more than 1 anthracycline has been used, then the cumulative dose must not exceed the equivalent of 350 mg/m² of doxorubicin. Patients with prior cumulative anthracycline exposure of greater than 368 mg/m2 daunorubicin (or equivalent) Prior exposure to >375 mg/m2 of doxorubicin or liposomal doxorubicin. Time to treatment failure from doxorubicin containing regimen ? 12 months if previously treated with doxorubicin. Prior epirubicin exposure of > 600 mg/m2. Prior therapy with anthracyclines exceeding the following doses (subjects will be discontinued at 600 mg/m2 lifetime dose irrespective of the number of ThermoDox® cycles received): Free (i.e., non-liposomal) or liposomal doxorubicin > 450 mg/m2 Free epirubicin > 900 mg/m2. Prior cumulative doxorubicin dose > 300 mg/m^2 Patients with prior cumulative anthracycline exposure of greater than 368 mg/m2 daunorubicin (or equivalent) Prior treatment with anthracyclines at cumulative doses of 450 mg/m² or more for doxorubicin or 900 mg/m² or more for epirubicin Cohort 2: Soft tissue sarcoma of intermediate or high grade with evidence of disease progression by either CT or MRI scan, or clinical judgment on or after the last cancer therapy within 6 months prior to the start of study treatment. Relapsed or refractory (lack of response) to ?1 course of systemic therapy regimen(s), excluding adjuvant or neoadjuvant chemotherapy, and is incurable by either surgery or radiation. Patients who have previously received anthracyclines are eligible if cumulative exposure is <375 mg/m2 for doxorubicin and liposomal doxorubicin or <675 mg/m2 for EPI. Prior exposure to >375 mg/m2 of doxorubicin or liposomal doxorubicin or ?675 mg/m2 of EPI. Chemotherapy must be planned for at least 4 cycles of full-dose anthracycline or taxane based chemotherapy regimen\r\n* Defined as one of the following regimens: \r\n** Adriamycin 60 mg/m2 with cyclophosphamide 600 mg/m2 \r\n** Epirubicin 90-100 mg/m2 with cyclophosphamide 600 mg/m2 \r\n** Doxorubicin 50 mg/m2 with 5-fluroruacil 500 mg/m2 and cyclophosphamide 500 mg/m2 \r\n** Paclitaxel 80 mg-90/m2 weekly (every three weeks constitute a cycle), or 175 mg/m2 every 2-3 weeks as a single agent \r\n** Docetaxel 100 mg/m2 as a single agent \r\n** Docetaxel 75 mg/m2 with cyclophosphamide 600 mg/m2 \r\n** Docetaxel 75 mg/m2 with carboplatin area under the curve (AUC) of 6 and traztuzumab at standard doses\r\n* Concurrent traztuzumab at standard doses is allowed\r\n* Concurrent pertuzumab at standard doses is allowed\r\n* Administration of chemotherapy on a dose dense schedule is allowed as clinically indicated Lifetime cumulative anthracycline dose: >= 300 mg/m^2 without the protection of dexrazoxane (Zinecard) therapy If in Arm D (doxorubicin and cyclophosphamide), patients with prior cumulative doxorubicin dose of >= 260 mg/m^2 Scheduled to receive chemotherapy with an anthracycline (doxorubicin [doxorubicin hydrochloride] or epirubicin [epirubicin hydrochloride]) Prior exposure to more than 360 mg/m^2 doxorubicin, more than 120 mg/m^2 mitoxantrone, or more than 90 mg/m^2 idarubicin, or elevated baseline cardiac troponin I Prior exposure to anthracyclines at a cumulative dose of doxorubicin (or equivalent) > 450 mg/m²