Chairman Bob Dole (R-Kan.) yesterday proposed to his Senate Finance Committee nearly $1 billion more in social program cuts than President Reagan has recommended. He would gain on the president in part by increasing premiums for the optional part of Medicare and making the elderly pay more from their own pockets before Medicare benefits kick in.

Under the Dole plan, so-called Medicare Part B premiums, now $9.60 but soon to rise to $11 a month, would in future be increased by whatever amount is needed to cover 25 percent of the cost of the optional Part B (out-of-hospital doctor bill) program.

And the amount the patient would have to pay before Part B benefits start would be increased from $60 annually to $75.

Another part of the Dole proposal could mean lower federal Medicaid payments for Maryland and the District of Columbia by reducing the minimum federal Medicaid reimbursement to any state from the current 50 percent to 40 percent. The District would drop to about 40 percent and Maryland to about 48 percent if Dole's proposal were accepted.

For the most part the Dole plan, which Sen. Daniel Patrick Moynihan (D-N.Y.) and others said is likely to win committee approval next week without much change, endorsed Reagan requests for cuts in Social Security, welfare, unemployment insurance and medical programs.

But the Dole plan would make some important changes in Reagn requests. It would junk Reagan's plan to wipe out doctor "peer review" groups (PSROs) that review medical practices in an attempt to restain Medicare and Medicaid costs.

It drops a Reagan request that people on unemployment insurance be required to take any available job at the minimum wage after they have received 13 weeks of benefits, instead of having the option (as they have now in many states) of holding out for a job similar to what they previously held.

In place of Reagan's request that the states be required to install "workfare" programs making welfare clients work off part of their monthly benefits, it merely gives the states the option of installing "workfare" if they choose. House public assistance subcommittee Chairman Fortney H. (Pete) Stark (D-Calif.) also has suggested an optional rather than mandatory approach.

The Dole plan drops Reagan's proposal for a national data bank on welfare clients and substantially changes his proposals to combine assorted welfare and child health programs into several large block grants.

It adds provisions (saving $700 million) that Medicare will only pay bills for kidney patients and retired federal employes after their existing private health insurance and retired government employes' insurance has first paid a share.

Overall, the Dole plan would save $10.4 billion in fiscal 1982, compared with Reagan's $9.6 billion request.The Dole plan approves with some changes Reagan's plans to phase out Social Security student benefits, eliminates the $122 minimum benefit for both future and current beneficiaries, tightens disability eligibility, and makes major cutbacks in unemployment insurnace, welfare and trade adjustment assistance.

It caps the increase for Medicaid next year at 9 percent instead of the president's 5 percent, but would recapture part of the lost savings by lowering the floor on reimbursement. And it excludes child welfare, foster care and adoption subsidies from the proposed block grants and keeps them as separate programs.