Part 2 provides additional data on the safety, toxicity and pharmacokinetics of CD4-IgG2 when given in multiple doses. Patients receive the highest safe dose (MTD) as established in Part 1. Treatment is given intravenously once weekly at Weeks 0, 1, 2, and 3. If insufficient activity is seen at this dose level, 6 additional patients will be enrolled at a higher dose level. Patients who participate in Part 1 may enroll in Part 2 provided they are followed for at least 3 months and meet inclusion criteria for Part 2. If any patient experiences a life-threatening condition due to CD4-IgG2, the study will stop. [AS PER AMENDMENT 4/25/00: Cohort II receives twice the dose of Cohort I intravenously once weekly at Weeks 0, 1, 2 and 3. Pharmacokinetic samples are obtained at pre-dose and 1 hour after the doses are administered at Weeks 0, 1, and 2; and pre-dose, 1 hour, 24 hours, and Days 3, 7, and 14 after the dose are administered at Week 3. An overnight stay in the hospital is recommended for the first 24 hours. At Weeks 0, 1, 2, and 3, virology testing including HIV-1 RNA is performed with each infusion of CD4-IgG. Follow-up monitoring of patients is done once a month for 4 months for patients in Cohort II.]