More Savings, More Choice Prescription Drug Act of 2002 - Amends title XVIII (Medicare) of the Social Security Act (SSA) to add a new part D (Voluntary Prescription Drug Benefit Program) to entitle each individual who is entitled to benefits under Medicare part A (Hospital Insurance) or is enrolled under Medicare part B (Supplementary Medical Insurance) to obtain qualified prescription drug coverage, with premium and cost-sharing subsidies for low-income individuals. Creates within the Federal Supplementary Medical Insurance Trust Fund the Medicare Prescription Drug Account for purposes of the new program. Amends SSA title XVIII (Medicare) part C (Medicare+Choice) to prohibit a Medicare+Choice organization from offering prescription drug coverage (other than that required under parts A and B) to an enrollee under a Medicare+Choice plan unless such drug coverage is at least qualified prescription drug coverage, and specified requirements of this Act are met.

Amends SSA title XIX (Medicaid) to: (1) require State Medicaid plans to provide for making eligibility determinations for premium and cost-sharing subsidies with regard to the Medicare prescription drug benefit for low-income Medicare beneficiaries; (2) provide for phased-in Federal assumption of Medicaid prescription drug costs for dually-eligible Medicare and Medicaid beneficiaries; (3) require continued Medicaid payment for such an individual to the extent payment is not made under the prescription drug plan or the Medicare+Choice plan selected by the individual; and (4) provide for Medicaid prescription drug coverage by territories.

Prescribes conditions and limitations for prescription drug coverage by new Medicare supplemental (Medigap) policies.