NEW YORK (CNN/Money) - The next stage in the battle over Social Security reform begins Tuesday on Capitol Hill, as experts come before the Senate Finance Committee to debate how best to achieve solvency in the system -- with and without individual investment accounts.

Committee chairman Charles Grassley (R-Iowa) has said that he would begin drafting legislation after the hearing and would like to have a bill ready by July, even if that meant it would only garner the support of the committee's Republicans, according to media reports.

There are 11 Republicans and nine Democrats on the committee.

On Tuesday, MFS chairman Robert Pozen, a Democrat who served on the President's Commission to Strengthen Social Security, will address the committee.

Pozen's suggested fix for solvency involves a different way of calculating starting benefits for new retirees known as progressive indexing. The proposal has gotten a lot of mention from the White House as one of the ideas "on the table" for consideration.

Currently, starting benefits for retirees at all income levels are linked -- or indexed -- to wage growth. To help the system achieve solvency, there have been proposals to change the indexing of starting benefits to the growth in prices, which tend to rise more slowly than wages.

Pozen's proposal uses both: The starting benefits of lower income workers would continue to be indexed to wage growth, while the starting benefits of higher income workers would be indexed to price growth. For middle-income workers, a combination of both indexes would be used.

Because middle and high-income workers would see a slower rate of growth in their benefits than is currently promised, Pozen has said there could be a "sweetener" to make the switch politically attractive.

One such sweetener might be adding individual investment accounts. If that's the route lawmakers choose, he has proposed allowing all workers to divert up to 2 percentage points of their payroll taxes into the accounts.

Other witnesses testifying before the Senate Finance Committee on Tuesday include two proponents of individual accounts: Michael Tanner, director of the Cato Institute's Project for Social Security Choice; and Peter Ferrara, a senior fellow with the Institute for Policy Innovation.

Also on the panel are two opponents of accounts: Peter Orszag, a senior fellow of economic studies at the Brookings Institution; and Joan Entmacher, vice president for family economic security at the National Women's Law Center.

Rather than focusing on individual accounts, Orszag told CNN's politcial unit that he believes the focus should be on improving existing accounts, like 401(k)s and IRAs.

"We're not fully using those accounts and they're not working as well as they could," said Orszag, who consults with finance ranking member Max Baucus (D-Montana) on the issue. "Let's take those accounts we already have and make them work better, rather than creating a new system of accounts."

Grassley's plan to have a bill to present to the Senate floor by summer will almost certainly be tested along the way. Democrats have been strongly unified in their opposition to President Bush's call for Social Security reform that includes individual investment accounts. Some Republicans, like finance committee member Olympia Snowe (R-Maine), have opposed adding accounts if they're financed by payroll taxes.

Grassley, according to media reports, has said he is open to all ideas, even if that means the focus is on reform is solvency and doesn't include individual accounts.

The Senate hearing on Tuesday marks what many media reports identify as the next stage in the battle over Social Security. Meanwhile, President Bush this week is wrapping up his 60-day, 60-stop Social Security tour.