While the Internal Revenue Service and tax experts in the private sector continue their efforts to figure out all the implications of the huge tax bill President Reagan just signed, tax policy-makers in the Treasury Department are making plans for a whole new legislative package -- a bill called "the second tax bill." Treasury officials and staffers from the tax-writing committees on Capitol Hill plan to work out details of the measure soon after Congress goes back into session on Sept. 9.

Treasury officials say they'd be just as happy without the new bill. But the measure is important to Senate Finance Committee Chairman Robert J. Dole (R-Kan.), who promised his colleagues they'd have a second bill this session on which to hang amendments that Dole didn't want added to the earlier legislation. The administration will go along -- but will fight to keep the new bill from cutting significantly into federal revenues.

The new legislation -- a separate bill from the one being drafted to correct minor errors in the law that was just passed -- will package a dozen or so miscellaneous provisions, probably including relaxation of withholding taxes on gambling income and extension of shale oil producers' credits.