The Reagan administration is considering asking Congress to reduce the so-called marriage penalty in the tax code, under which many married couples with two incomes pay more taxes than they would if both were single.

More than 200 members of the House -- nearly a majority -- have already signed on as cosponsors of a bill to make such a change, which would affect millions of families.

Norman Ture, new Treasury undersecretary for tax policy, said yesterday that the marriage penalty was "the very sort of thing" that would be included in a second set of tax proposals which the administration is considering for submission to Congress after the general tax cut the president will recommend next week. The president, sources said, will probably refer to these other ideas in his speech next week but will not be specific.

The administration hopes that, with a second bill promised, Congress will not load up the first with pet provisions, but will pass it fast.

Reagan's advisers have not yet decided what to include in a second bill. But they are considering several forms of tax relief on interest and dividend income and numerous other proposals long popular on Capitol Hill.

Chief among those under consideration:

Elimination or reduction of the marriage penalty. This could cost the Treasury up to $10 billion a year.

Tuition tax credits, which Reagan himself has endorsed. A tuition tax credit bill previously passed by the House would have cost about $1 billion.

Deductions for charitable contributions even if other deductions are not itemized: $2 billion.

"Amelioration" of what critics are the double taxation of dividends under present law, first as corporate profit, then as individual income: potential cost up to $20 billion.

Separate taxation of interest income, thereby lowering the marginal rate of tax on much of it: cost up to $17 billion.

A tax credit for research and development: $1 billion.

Tax relief for Americans working overseas: $500 million.

Corporate tax rate reductions: a drop of one percentage point would cost about $2 billion.

These measures could be very substantial revenue losers and, if passed by Congress, would eat into the money available for the administration's preferred tax cuts: across-the-board reductions in personal tax rates, and more generous depreciation allowances for business.

The president said last week in his televised address to the nation that the Kemp-Roth proposal to cut personal tax rates by 10 percent a year for three years will be part of his economic program.

The administration has apparently not yet decided whether the second bill would include some tax increases to offset the cuts, or whether it would add to the revenue cost of the main measures. Congressional sources doubt that members will wait for a second bill before pushing their own tax favorities. They are more likely to tack their favored measures onto the first bill, sources said this week.

Of the additional measures, Ture said yesterday that the administration "may want to talk about them very early on." He and budget director David Stockman have characterized the extra proposals as "non-economic." Ture, a well-known "supply sider," believes that cutting marginal tax rates, as in Kemp-Roth, will have a dynamic effect on the economy which is different from that of other tax cuts.

The administration plans "extensive discussions with the tax-writing committees" on the Hill to "explain the rationale" behind the two-tier approach.It has yet to order its priorities for the second round of proposals, and will consider all those "concerns that have had substantial support" from Congress in the past, Ture said.