Cancer and Blood Pressure Management, CARISMA Study

Inclusion Criteria: * English speaking * Patient must have histologically or cytologically-proven advanced metastatic renal cell cancer (mRCC) or medullary thyroid cancer initially treated with anti-angiogenic tyrosine kinase inhibitors (AA-TKIs) including: sunitinib, sorafenib, pazopanib, cabozantinib, lenvatinib, vandetanib, or axitinib) * NOTE: If patient has a severe sulfa allergy (e.g. Stevens Johnson reaction), then alternative non-sulfa medications can be considered in consultation with the C-BAC. Patient with a noted severe allergic reactions to medications listed in the algorithms is not necessarily excluded from this trial, as alternative medications could be considered in consultation with the C-BAC. Moreover, the patient treated with pre-existing medications that may interact with proposed BP medications is not necessarily excluded, as alternative medications exist. The clinical significance of any potential drug interactions can also be addressed with the C-BAC. * Prior exposure to another AA-TKI is permissible. Concurrent or prior treatment with immunotherapy is also permissible * Patient must have either clinical cardiovascular (CV) disease or evidence of increased CV risk as defined by one or more of the following: * Clinical CV disease (history of myocardial infarction \[MI\] acute coronary syndrome, coronary revascularization, carotid endarterectomy or stenting greater than 3 months prior to registration, peripheral artery disease, cerebrovascular accident greater than 3 months prior to registration, abdominal aortic aneurysm or heart failure \[HF\]) * An American College of Cardiology/American Heart Association (ACC/AHA) CV risk score of at least 10% * Chronic kidney disease (defined as an estimated glomerular filtration rate \[eGFR\] between 30 and 60 ml/min per 1.73 m\^2). Dialysis patients and patients with an eGFR \< 30 ml/min/1.73m\^2 will be excluded. eGFR will be calculated according to the Chronic Kidney Disease Epidemiology Collaboration (CKD-Epi) equation * Patient must have systolic blood pressure (SBP) \>= 130 mmHg on two or more occasions according to any in-clinic visit in the 12 weeks prior to or during their initial 4 weeks of treatment with an AA-TKI. Patient who have a prior diagnosis of hypertension or on pre-existing anti-hypertensive medications are eligible for enrollment. However, patient must not be on more than 3 baseline blood pressure medications at time of entry * NOTE: If a patient has a single elevated SBP \>= 130mmHg but not on repeat assessment, an additional SBP assessment should be performed to confirm ineligibility * Patient must agree to comply with performing home blood pressure monitoring using an Omron7250 oscillometric monitor at home, or equivalent models * Women of childbearing potential and sexually active males must be strongly advised to use accepted and effective methods of contraception or to abstain from sexual intercourse for the duration of their participation in the study * Patient must have internet access through a computer, tablet, or smart phone to use EASEE-PRO and home BP monitoring. A valid phone number to receive text messages and email address are also necessary * Leukocytes \>= 3,000/mcL (obtained within 14 days prior to registration) * Absolute neutrophil count \>= 1,500/mcL (obtained within 14 days prior to registration) * Platelets \>= 100,000/mcL (obtained within 14 days prior to registration) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal (ULN) (obtained within 14 days prior to registration) * Patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patient with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patient with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression * Patient with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate CNS specific treatment is not required and is unlikely to be required during the first cycle of therapy * Patient with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status 0-2 Exclusion Criteria: * Patient must not have end-stage renal failure on dialysis, history of repeated hyperkalemia with a potassium \> 5.5 mEq/l, or have a kidney transplant, or an eGFR \< 30 ml/min/1.73 m\^2 * Patient must not have coronary artery bypass grafting, MI acute coronary syndrome severe/unstable angina, stroke, transient ischemic attack, clinically significant bleeding requiring hospitalization or pulmonary embolism within 3 months prior to registration * Patient must not have brain surgery or radiotherapy within 2 weeks prior to registration * Patient must not have uncontrolled blood pressure defined by SBP \> 160 mmHg on three or more antihypertensives prior to TKI initiation * Patient with an arm circumference too large (\> 50 cm) or small (\< 17 cm) to allow accurate BP measurement with available devices will not be eligible * Women must not be pregnant or breast-feeding due to the potential harm to an unborn fetus and possible risk for adverse events in nursing infants with some anti-hypertensives, including angiotensin receptor blockers. All females of childbearing potential must have a blood test or urine study within 14 days prior to registration to rule out pregnancy. A female of childbearing potential is defined as any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: has achieved menarche at some point, has not undergone a hysterectomy or bilateral oophorectomy; or has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months)