Eligibility Criteria:
Inclusion Criteria for Step 1:
1. HIV-1 infection
2. Biopsy diagnostic of KS at any time prior to study entry.
3. Current KS stage T1 using ACTG criteria.
4. A minimum of five indicator KS cutaneous marker lesions (or if fewer than five marker lesions are available, the total surface area of the marker lesion(s) must be \>=700 mm\^2) plus an additional two lesions greater or equal to 4x4 mm that are accessible for punch biopsy.
5. CD4+ lymphocyte cell count obtained within 28 days prior to study entry at a DAIDS-approved laboratory.
6. Certain laboratory values, as defined in the protocol, obtained within 14 days prior to study entry.
7. Female study volunteers of reproductive potential must have a negative serum or urine pregnancy test with a sensitivity of 15-25 mIU/mL performed within 48 hours before initiating the protocol-specified medications.
8. All participants must agree not to participate in a conception process (active attempt to become pregnant or to impregnate, donate sperm, in vitro fertilization).
9. If participating in sexual activity that could lead to pregnancy, participant must agree that two reliable forms of contraceptives will be used simultaneously while receiving protocol-specified medications, and for 12 weeks after stopping the medications. Study volunteers who are not of reproductive potential (women who have been post-menopausal for at least 24 consecutive months or have undergone hysterectomy and/or bilateral oophorectomy or men who have documented azoospermia) are eligible without requiring the use of contraceptives.
10. Ability to swallow oral medications and adequate venous access.
11. Karnofsky performance status \>= 60 within 28 days prior to entry.
12. Ability and willingness of participant or legal guardian/representative to provide informed consent.
Exclusion Criteria for Step 1:
1. Current chronic, acute, or recurrent serious infections for which the participant has not completed at least 14 days of therapy prior to study entry and/or is not clinically stable.
2. Serious illness requiring systemic treatment and/or hospitalization within 14 days prior to entry.
3. Current or history of known pulmonary fibrosis, chronic obstructive pulmonary disease (COPD), emphysema, bronchiectasis, or diffuse or significant local radiographic interstitial infiltrates on chest x-ray (CXR) or computed axial tomography (CT) scan.
4. Oxygen saturation less than 90% and/or exercise desaturation greater than 4% within 14 days prior to study enrollment.
5. Grade \>=3 peripheral neuropathy (PN) at entry.
6. Breastfeeding.
7. Receipt of ART for more than 42 days immediately prior to entry.
8. Prior or current systemic or locally administered chemotherapy.
9. Prior or current radiation therapy.
10. Prior or current immunotherapy, e.g., interferon alfa.
11. Corticosteroid use at doses above those given as replacement therapy for adrenal insufficiency within the last 30 days prior to study entry.
12. Any immunomodulator, HIV vaccine, live attenuated vaccines, or other investigational therapy or investigational vaccine within 30 days prior to study entry.
13. Known allergy/sensitivity or any hypersensitivity to components of study drugs or their formulation.
14. Active drug or alcohol use or dependence that would interfere with adherence to study requirements.
15. Current or anticipated receipt of any of the prohibited medications listed in section 5.5.2 of the protocol.
16. In the opinion of the investigator, any psychological or social condition, or addictive disorder that would preclude compliance with the protocol.
Inclusion Criteria for Step 2:
1. IERC-confirmed complete response (CR) or partial response (PR) to the chemotherapy regimen used in Step 1.
2. IERC-confirmed KS progression at least 12 weeks after the last dose of Step 1 chemotherapy.
3. Fewer than 72 weeks after Step 1 entry
4. Certain laboratory values, as defined in the protocol, obtained within 14 days prior to Step 2 entry.
5. For females of reproductive potential or females not of reproductive potential who do not have required documentation, negative serum or urine pregnancy test with a sensitivity of 15-25 mIU/mL within 7 days prior to Step 2 entry.
6. Karnofsky performance status \>=50 within 28 days prior to Step 2
7. All participants must agree not to participate in a conception process (active attempt to become pregnant or to impregnate, donate sperm, in vitro fertilization).
Exclusion Criteria Step 2:
1. Current chronic, acute, or recurrent infections that are serious, in the opinion of the site investigator, for which the participant has not completed at least 14 days of therapy prior to Step 2 entry and/or is not clinically stable.
2. Severe toxicity to the chemotherapy regimen used in Step 1 requiring discontinuation of study chemotherapy.
3. Serious illness, other than progressive KS, requiring systemic treatment and/or hospitalization within 14 days prior to Step 2 entry.
4. For volunteers who received bleomycin in Step 1
* Development of of pulmonary fibrosis, COPD, emphysema, bronchiectasis, and diffuse or significant local radiographic interstitial infiltrates on CXR or CT scan that in the opinion of the site investigator would exclude bleomycin use.
* Oxygen saturation less than 90% or exercise desaturation greater than 4% within the last 30 days prior to Step 2 entry.
5. For volunteers who received Vincristine or Paclitaxel in Step 1, Grade \>=3 PN at Step 2 entry.
6. Breastfeeding.
7. Other concurrent chemotherapy, immunotherapy, or radiotherapy.
8. Systemic corticosteroid use at doses above those given as replacement therapy for adrenal insufficiency within 30 days of Step 2 entry.
9. Receipt of Etoposide (ET) in Step 1.
Inclusion Criteria Step 3:
1. (a) IERC-confirmed KS progression at any time during Step 1 chemotherapy, or (b) IERC-confirmed KS progression fewer than 12 weeks after the last chemotherapy dose in Step 1 in participants who have had an IERC-confirmed CR or PR, or (c) IERC-confirmed KS progression following Step 1 chemotherapy, without any prior response, or (d) IERC-confirmed KS progression in Step 2, or (d) with concurrence of the CMC, there is dose-limiting toxicity after receiving fewer than four cycles of chemotherapy in Step 1 or Step 2, in the absence of a CR or PR, or (e) volunteers otherwise eligible for Step 2 who, in the opinion of the investigator and with concurrence of the CMC, are unlikely to benefit from another course of the same chemotherapy received in Step 1.
2. Fewer than 72 weeks after Step 1 entry.
3. Certain laboratory values, as defined in the protocol, obtained within 14 days prior to Step 3 entry.
4. For females of reproductive potential or females not of reproductive potential who do not have required documentation, negative serum or urine pregnancy test with a sensitivity of 15-25 mIU/mL within 7 days prior to Step 3 entry.
5. Karnofsky performance status \>=50 within 28 days prior to Step 3 entry.
6. All participants must agree not to participate in a conception process (active attempt to become pregnant or to impregnate, donate sperm, in vitro fertilization).
Exclusion Criteria Step 3:
1. Current chronic, acute, or recurrent infections that are serious, in the opinion of the site investigator, for which the participant has not completed at least 14 days of therapy prior to Step 3 entry and/or is not clinically stable.
2. Serious illness, other than progressive KS, requiring systemic treatment and/or hospitalization within 14 days prior to Step 3 entry.
3. Eligible for Step 2 entry.
4. For participants who did not receive bleomycin in Step 1 or Step 2:
* Development of pulmonary fibrosis, COPD, emphysema, bronchiectasis, and diffuse or significant local radiographic interstitial infiltrates on CXR or CT scan that in the opinion of the site investigator would exclude bleomycin use.
* Oxygen saturation less than 90% or exercise desaturation greater than 4% within the last 30 days prior to Step 3 entry.
5. Grade \>=3 PN at Step 3 entry.
6. Breastfeeding
7. Other concurrent chemotherapy, immunotherapy, or radiotherapy.
8. Systemic corticosteroid use at doses above those given as replacement therapy for adrenal insufficiency within 30 days of Step 3 entry.
Inclusion Criteria Step 4:
1. (a) IERC-confirmed KS progression in Step 3, or (b) With concurrence of the CMC, dose-limiting toxicity after receiving fewer than four cycles of chemotherapy in Step 3, in the absence of a CR or PR, or (c) Current receipt of ET in Step 3.
2. Fewer than 72 weeks after Step 1 entry.
3. Certain laboratory values, as defined in the protocol, obtained within 14 days prior to Step 4 entry.
4. For females of reproductive potential or females not of reproductive potential who do not have required documentation, negative serum or urine pregnancy test with a sensitivity of 15-25 mIU/mL within 7 days prior to Step 4 entry.
5. Karnofsky performance status \>=50 within 28 days prior to Step 4 entry.
6. All participants must agree not to participate in a conception process (active attempt to become pregnant or to impregnate, donate sperm, in vitro fertilization).
7. Receipt of ET in Step 1, Step 2, or Step 3.
Exclusion Criteria Step 4:
1. Current chronic, acute, or recurrent infections that are serious, in the opinion of the site investigator, for which the participant has not completed at least 14 days of therapy prior to Step 4 entry and/or is not clinically stable.
2. Serious illness, other than progressive KS, requiring systemic treatment and/or hospitalization within 14 days prior to Step 4 entry.
3. For participants who did not receive bleomycin in Step 1, Step 2, or Step 3:
* Development of pulmonary fibrosis, COPD, emphysema, bronchiectasis, and diffuse or significant local radiographic interstitial infiltrates on CXR or CT scan that in the opinion of the site investigator would exclude bleomycin use.
* Oxygen saturation less than 90% or exercise desaturation greater than 4% within the last 30 days prior to Step 4 entry.
4. Grade \>=3 PN at Step 4 entry.
5. Breastfeeding.
6. Other concurrent chemotherapy, immunotherapy, or radiotherapy.
7. Systemic corticosteroid use at doses above those given as replacement therapy for adrenal insufficiency within 30 days of Step 4 entry.