At least a dozen “super PACs” are setting up to back individual Republican candidates for the United States Senate, challenging the strategic and financial dominance that Karl Rove and the group he co-founded, American Crossroads, have enjoyed ever since the Supreme Court’s Citizens United decision in 2010 cleared the way for unlimited independent spending.

In wooing donors, the new groups — in states like Texas, Iowa, West Virginia and Louisiana — are exploiting Crossroads’ poor showing in 2012, when $300 million spent by the super PAC and a sister nonprofit group yielded few victories. Some are suggesting that Crossroads’ deep ties to the Republican establishment and recent clashes with conservative activists are a potential liability for Republican incumbents facing Tea Party challengers.

“Certainly I think there’s a level of frustration with the state of things in D.C.,” said Randy Cubriel, an Austin lobbyist who formed Texans for a Conservative Majority, a new super PAC, to back Senator John Cornyn. Earlier this year, the group reported raising $2 million from the Texas homebuilder Bob J. Perry, one of Crossroads’ top donors during the 2012 cycle, who died in April.