The Dow was up 49 points to 12,988 shortly after noon. Earlier in the morning, it rose as high as 12,996. On Tuesday it briefly traded above 13,000 for the first time in nearly four years.
The broader Standard & Poor's 500 was up three points to 1,361, and the Nasdaq composite was up 19 points to 2,952.
The gains were uneven. Seven of the 10 industry groups in the S&P 500 rose, led by financials.
Grocery store operator Safeway Inc. plunged 10 percent after reporting a 6 percent drop in profit. Grocers are struggling with rising prices for food and fuel while dealing with cost-conscious shoppers.
Kohl's, the department store chain, sank 5 percent after weak holiday sales forced it to miss analysts' estimates for revenue and per-share earnings. Retailers are struggling to lure cash-strapped customers to keep spending and are being forced to slash prices, which might persuade more customers to walk through the door but also cuts into profit margins.
The market has been yanked up and down this year by incremental headlines out of Greece as the country's lawmakers and its lenders wrestled over a deal that would keep the country from defaulting on debt next month but also require it to cut the profligate public spending that its citizens have grown used to.
Earlier this week Greece locked down terms of its second bailout but it doesn't have the money yet. The terms of the deal still need to be validated by the end of March, meaning the market could continue to fluctuate on small changes in the deal-making process.
David Trone, managing director of JMP Securities, said financial stocks were up on the relative calm in Greece. U.S. bank stocks had plummeted last year over fears about their exposure to European debt.
Otherwise, Thursday's news out of Greece was too incremental to move the market much one way or the other. "Investors aren't feeling any happier or any worse than they were yesterday," Trone said.
For the most part, U.S. stocks have been rising since Thanksgiving, as the most potent fears of last summer — that the country would enter another recession, and that the European debt crisis would prove catastrophic to the U.S. — have dissipated.
The market has yet to settle into a definitive trend, however. In the 35 completed trading days so far this year, the Dow has risen on 20 and fallen on 15.
The yield on the 10-year Treasury note rose to 2.02 percent from 2 percent late Wednesday, another sign that investors are putting more money into stocks rather than the safe-haven government bonds.
There have been signs that the U.S. economy is improving — including Thursday's report that the number of people seeking unemployment aid last week was unchanged, at its lowest point in four years.
There are also concerns that the nascent recovery could be derailed by a jobless rate that remains roughly double what economists consider full employment, and gas prices that are higher than they've ever been at this time of year. A gallon of regular gas costs $3.61, on average, up from $3.19 a year ago as tensions mount over Iran's nuclear program.
Among other stocks making big moves, Hewlett-Packard dropped 4 percent after issuing a disappointing profit outlook and reporting a 7 percent decline in sales. New CEO Meg Whitman pleaded for patience from investors as she described internal challenges and other problems that contributed to a decline in earnings at one of the world's largest technology companies.