ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): No evidence of prior malignancy except adequately treated non-melanoma skin cancer, in situ cervical carcinoma, or any surgically- or radiation-cured malignancy continuously disease free for >= years so as not to interfere with interpretation of radiographic response ELIGIBILITY CRITERIA - PHASE II (ARM D): No evidence of prior malignancy except adequately treated non-melanoma skin cancer, in situ cervical carcinoma, or any surgically- or radiation-cured malignancy continuously disease free for >= years so as not to interfere with interpretation of radiographic response Other invasive malignancies within the last years, except non-melanoma skin cancer and localized cured prostate, cervical cancer, and ductal breast carcinoma in situ (DCIS) Diagnosis of another malignancy within years before the first dose of cabozantinib, except for superficial skin cancers, or localized, low grade tumors deemed cured and not treated with systemic therapy Diagnosis of another malignancy within years before the first dose of study treatment, except for superficial skin cancers, or localized, low grade tumors deemed cured and not treated with systemic therapy Previous or concomitant malignancies at other sites, except effectively treated non-melanoma skin cancers, carcinoma in situ of the cervix, ductal carcinoma in situ or effectively treated malignancy that has been in remission for more than years and is considered to be cured AND no additional therapy is ongoing and required during the study period with the exception of bisphosphonates and anti-androgens and/or gonadorelin analogues for the treatment of prostate cancer are permitted; subjects with other active malignancy requiring concurrent intervention are excluded Subjects with known active central nervous system metastasis, glioma and nervous system malignancies including carcinomatous meningitis or other invasive malignancy within years except for noninvasive malignancies such as cervical carcinoma in situ, non-melanomatous carcinoma of the skin or ductal carcinoma in situ of the breast that has/have been surgically cured. Previous or concomitant malignancies at other sites, except effectively treated non-melanoma skin cancers, ductal carcinoma in situ or effectively treated malignancy that has been in remission for more than years and is considered to be cured Treatment for other carcinomas within the last three years, except cured non-melanoma skin and treated in-situ cervical cancer Active malignancies (that is, requiring treatment change in the last months) other than urothelial cancer (except skin cancers within the last months that is considered completely cured) Evidence within years of the start of study treatment of another malignancy which required systemic treatment except for breast ductal carcinoma-in situ, cured non-melanoma skin cancer, or cured in situ cervical carcinoma. Current or previous malignant disease (other than colorectal cancer) within the last years; with the exception of the following if considered curatively treated: non-melanoma skin cancer(s), carcinoma in situ of the cervix, and ductal carcinoma in situ; subjects with another active malignancy requiring concurrent anti-cancer intervention are excluded; (Note the following does not exclude: effectively treated malignancy that has been in remission for more than years and is considered to be cured AND no additional anti-cancer therapy is ongoing and required during the study period) Diagnosis of another malignancy within years before the first dose of study treatment, except for superficial skin cancers, or localized, low grade tumors deemed cured and not treated with systemic therapy; malignancy felt by investigator to potentially affect subject survival or ability to evaluate disease response Any previous history of another malignancy (other than cured basal cell or squamous cell carcinoma of the skin or cured in-situ carcinoma) within years of study entry; Previous or concomitant malignancies at other sites, except effectively treated non-melanoma skin cancers, carcinoma in situ of the cervix, ductal carcinoma in situ or effectively treated malignancy that has been in remission for more than years and is considered to be cured History of recent malignancies < years (except for cured non-melanomatous skin cancer or cured cervical carcinoma in situ) Other invasive malignancy within years except for noninvasive malignancies such as cervical carcinoma in situ, non-melanomatous carcinoma of the skin or ductal carcinoma in situ of the breast that has/have been surgically cured Other invasive malignancies within years except for noninvasive malignancies such as cervical carcinoma in situ, non-melanomatous carcinoma of the skin, or ductal carcinoma in situ of the breast, etc. that has/have been surgically cured Evidence within years of the start of study treatment of another malignancy which required systemic treatment except for cured nonmelanoma skin cancer or cured in situ cervical carcinoma Other malignancy within years, except for noninvasive malignancies such as cervical carcinoma in situ (CIS), non-melanomatous carcinoma of the skin or ductal carcinoma in situ (DCIS) of the breast that has/have been surgically cured, or prior malignancy considered by the investigator to be of low likelihood for recurrence No evidence of prior malignancy except adequately treated non-melanoma skin cancer, in situ cervical carcinoma or any surgically- or radiation-cured malignancy continuously disease free for >= years so as not to interfere with interpretation of radiographic response RANDOMIZED PHASE II (ARMS K AND L): No evidence of prior malignancy except adequately treated non-melanoma skin cancer, in situ cervical carcinoma or any surgically- or radiation-cured malignancy continuously disease free for >= years so as not to interfere with interpretation of radiographic response Active malignancies (that is, requiring treatment change in the last months) other than urothelial cancer (except skin cancers within the last months that are considered completely cured) History of prior or concomitant malignancies (other than excised non-melanoma skin cancer or cured in situ cervical carcinoma) within years of study entry. History of prior malignancy, except for cured non-melanoma skin cancer, cured in situ cervical carcinoma, or other treated malignancies with no evidence of disease for at least three years Participant has had another active malignancy within the past years except for any cancer considered cured or non-melanoma carcinoma of the skin. Other malignancy except for treated and cured basal or squamous cell skin cancer, cured in situ cancers, or other cancer from which the patient has been disease-free for ? years. Subject who other invasive malignancy within years ( years for Arm A) except for noninvasive malignancies such as cervical carcinoma in situ, non-melanomatous carcinoma of the skin, ductal carcinoma in situ of the breast, or incidental histologic finding of prostate cancer (Ta or Tb using the TNM [tumor, nodes, metastasis] clinical staging system) that has/have been surgically cured. Other invasive malignancy within years prior to enrollment (localized prostate cancer, cervical carcinoma in situ, non-melanoma skin cancer, or ductal carcinoma in situ of the breast that has/have been surgically cured would not be exclusionary). other effectively treated malignancy that has been in remission for more than years and is considered to be cured Diagnosis of another malignancy within years of enrollment, except for superficial skin cancers, or localized, low grade tumors deemed cured and not treated with systemic therapy by the principal investigator Previous or concomitant malignancies at other sites, except effectively treated non-melanoma skin cancers, carcinoma in situ of the cervix, ductal carcinoma in situ or effectively treated malignancy that has been in remission for more than years and is considered to be cured in the opinion of investigator. History of other malignancies (except for cured non-melanomatous skin cancer or cured cervical carcinoma in situ, or malignancies with no evidence of disease and no treatment for > years) Concurrent active malignancy other than non-melanoma skin cancers or carcinoma-in-situ of the cervix, or presence of myelodysplastic or myeloproliferative disease; patients with prior malignancies with a disease-free interval of >= years are eligible; patients who have had prior malignancies within the past years but are considered to be cured with a low likelihood of recurrence may be eligible at the discretion of the principal investigator No prior or concurrent malignancies at other sites except for surgically cured carcinoma in situ of the cervix or nonmelanoma skin cancer History of a different cancer within the last years, except for nonmelanoma skin cancer, stage renal cell carcinoma, stage prostate cancers cured by local resection and any curatively treated carcinomas in situ Concomitant malignancy other than NSCLC that requires active therapy; prior malignancies are allowed as long as the disease is controlled and does not require ongoing therapy of any kind; prior therapy must have concluded at least year before treatment initiation on this protocol; exceptions are non-melanoma skin cancer, prostate cancer and prostatic intraepithelial neoplasia (PIN) treated with local intervention and deemed cured, cervical cancer and carcinoma in situ (CIS) treated with local intervention and deemed cured, and laryngeal cancer and CIS treated with local intervention and deemed cured Other invasive malignancy within years except for noninvasive malignancies such as cervical carcinoma in situ, in situ prostate cancer, non-melanomatous carcinoma of the skin, ductal carcinoma in situ of the breast that has been surgically cured Another invasive malignancy within years prior to enrollment except for localized prostate cancer, cervical carcinoma in situ, non-melanomatous carcinoma of the skin, or ductal carcinoma in situ of the breast that has/have been surgically cured Previous or concomitant malignancies at other sites, except effectively treated non-melanoma skin cancers, carcinoma in situ of the cervix, ductal carcinoma in situ or effectively treated malignancy that has been in remission for more than years and is considered to be cured. History of cancer within the last years, except for nonmelanoma skin cancer, stage renal cell carcinoma, stage prostate cancers cured by local resection and any curatively treated carcinomas in situ Other invasive malignancy within years except for noninvasive malignancies such as cervical carcinoma in situ, non-melanomatous carcinoma of the skin or ductal carcinoma in situ of the breast that has/have been surgically cured The patient has (or has had) previous or concomitant malignancies, except effectively treated malignancy that is considered by the investigator highly likely to have been cured. Treatment for other carcinomas within the last five years, except cured non-melanoma skin and treated in-situ cervical cancer