Hillary Rodham Clinton’s campaign has gotten commitments from four Democratic state parties, including the one in crucial proving ground of New Hampshire, to enter into joint fundraising agreements to begin raising money now, while the nominating battle is underway.

The four states reflect just a small fraction of the dozens of parties that Hillary for America has asked to sign up for such agreements. Many are still considering whether to join; some officials said they’re working through exactly how such arrangements would be carried out while the nominating fight is going on.

In addition to New Hampshire, the three other state parties that have already signed agreements with the Clinton campaign are in Virginia, Mississippi and Wisconsin, according to two people briefed on the issue, who weren’t authorized to speak publicly. Virginia, a critical general election battleground, is also home to Gov. Terry McAuliffe, Mrs. Clinton’s close friend and a former Democratic National Committee chairman.

Officials with Mrs. Clinton’s campaign declined repeated requests for comment.

But the move, according to officials with some state parties in discussions with the Clinton campaign, emerged in the wake of the U.S. Supreme Court decision in 2014 that struck down aggregate limits on how much donors are able to give to candidates and political parties. Mrs. Clinton’s aides have repeatedly put an emphasis on rebuilding state parties that have deteriorated in recent years.

It also has fallen into place as efforts to form a joint fundraising agreement between Mrs. Clinton’s campaign and the Democratic National Committee have repeatedly hit snags, amid concerns and distrust within the candidate’s campaign of the current party leadership in terms of controlling the money in a shared account. The D.N.C. is in theoretically neutral in the race, but has been accused of taking some actions that could benefit Mrs. Clinton, such as restricting the number of debates.