If you’re Senate Minority Leader Mitch McConnell (R-Ky.), it’s the problem you want.

The 41-seat Senate Republican Conference, barely strong enough to muster a filibuster and rolled on major legislation for much of the past year, is poised to grow its ranks in November. But an increase in power, while offering the GOP political relevancy and fresh opportunities to shape the agenda, could present McConnell with new leadership challenges as well.

In several competitive Senate races, Republicans have nominated, or are headed toward nominating, aggressive philosophical conservatives who are pointedly running against the GOP establishment. And yet a number of other seats that could turn Republican on Nov. 2 feature GOP candidates who might take centrist positions on key issues to reflect the politics of their Democratic-leaning states.

The potential for such a significant increase in ideological and regional diversity within the minority Conference, combined with the loss of some veteran Republican Senators moored in the ways and traditions of the chamber, poses both risks and rewards for McConnell and his accommodating, deliberate leadership style.

“Of course, diversity brings with it management issues. But it’s a nice problem to have,” Republican Conference Chairman Lamar Alexander (Tenn.) said. “It’s like having a corral full of new horses and they’re kicking, and they may even be biting each others’ necks, but they’re thoroughbreds and we’re really eager to get them.”

Exhibit A in the intra-Conference terrain that McConnell might have to navigate in the 112th Congress can be found close to home — literally. In Tuesday’s Kentucky GOP Senate primary, McConnell’s handpicked candidate to replace retiring Sen. Jim Bunning, Kentucky Secretary of State Trey Grayson, could lose to upstart conservative physician Rand Paul, the son of Rep. Ron Paul.

The Texas Republican has strong libertarian leanings, has never shown much regard for his party’s leadership in the House and often holds views anathema to conventional conservatives. Political observers familiar with the younger Paul say the two men are similar in their outlook, which, if true, could create headaches for McConnell given the power and opportunity to make national news available to even the most junior of Senators.

Paul — if he wins the primary and survives the general election — isn’t the only new conservative who could push the Republican Conference to be more openly confrontational and impolitic in tone, than McConnell and veteran GOP Senators are comfortable with. Former Rep. Pat Toomey (Pa.), who as Club for Growth president during the 2006 and 2008 cycles moved to purge GOP moderates, is another.

Attorney Mike Lee and businessman Tim Bridgewater, who took down Sen. Bob Bennett in Utah’s GOP nominating convention and will face off in a June 22 primary, as well as ex-Florida Speaker Marco Rubio, also are potential agitators. They could be similar to the bevy of liberal Democrats elected to the Senate since 2006, eager to make their mark and impatient with a leadership that they often see as too accommodating to the opposition and too wedded to procedural tradition.

But Sen. Jim DeMint, open about his displeasure with the GOP leadership, predicts there would be little infighting in a Republican Conference made larger by the addition of philosophically diverse individuals. The South Carolina Republican offered weak praise for McConnell, while arguing that the retirement of some longtime GOP Appropriations members would facilitate Republican unity around fiscal issues on which they already agree and which resonate with the voters.

“I think Mitch McConnell’s instincts are conservative, and he has to just pull together a consensus of our Conference. As that consensus comes back more to a center-right position, I think it will be easier for him,” said DeMint, who recently endorsed Paul and backed Rubio last year when Florida Gov. Charlie Crist was still a Republican and the leadership’s preferred candidate. “I don’t think there’s a big difference between Pennsylvania and South Carolina as far as what people are saying now. It’s not all the social and cultural issues. It’s stop spending, stop borrowing, stop taking over.”

But big gains for the Republicans in the midterm elections would mean the addition of at least a few moderates, not to mention some veteran lawmakers who might operate as institutional pragmatists. This could test Conference unity and McConnell’s ability to maintain the strategic discipline that the minority has exhibited for much of the past 15 months.

Moderate Rep. Mark Kirk could win Obama’s old Senate seat in Illinois, centrist Rep. Mike Castle is favored in Delaware, seven-term Rep. Roy Blunt is in the hunt in the swing state of Missouri, and ex-Rep. Rob Portman is running strong in Ohio, another bellwether. The Republican nominee in competitive Indiana, currently ahead in the polls, is lobbyist and former Sen. Dan Coats. The GOP is also primed to run well in swing states such as Colorado and New Hampshire. Meanwhile, the Republicans hope to be competitive in the Democratic-leaning states of California, Washington and Wisconsin.

Victories in any of these states could expand the moderate wing of the Republican Conference and increase the likelihood of friction with the conservatives. But senior Republican Senate aides, former GOP leadership aides and Members themselves say McConnell is ready.

“It will be a challenge, and he will be up to it,” said Bennett, a close confidant of McConnell. “Mike Castle is not going to be the kind of Senator that the new Senator from Utah will be — whoever it is. You navigate it by sitting down with the folks and talking through exactly what their goals are. … McConnell is as skillful at that as anybody I’ve ever seen. He’ll be just fine.”

McConnell’s backers say his biggest strength in leading a chamber where Members are prone to independence and, unlike the House, have the power to ignore leadership if they choose is that he listens first and talks second. According to a senior GOP aide, the Minority Leader never misses a caucus or Steering Committee lunch. “Foreign leaders could be in the Capitol, but he doesn’t miss a lunch. It’s that important to him,” this aide said.

The Kentuckian also works to cultivate outliers in his Conference. He does not always succeed, as evidenced by hostile relations with Bunning and DeMint, although he remains highly regarded by most in his Conference and throughout GOP circles in Washington, D.C.

GOP operatives familiar with McConnell expect that his successful courtship of Sen. Tom Coburn, a conservative Oklahoma Republican who regularly diverges from the Conference on spending issues and with whom he originally clashed, is likely to serve as model for how he’ll approach the incoming group of Members who see themselves as sent to D.C. by the tea party activists to shake things up.

McConnell’s method is to try to build a consensus around a Member’s idea, or at least find a way to push what that Member wants through existing channels. He’s also likely to manage committee assignments strategically, in an effort to prevent counterproductive political gamesmanship. For instance, he likely would not place a Member who wants to abolish earmarks on Appropriations.

The Minority Leader, Republicans say, is prepared for what lies ahead and is likely to act next cycle with an eye toward winning back the Senate in 2012. “The old Republican bulls have been patiently awaiting a return to power. They are going to be shocked to find out the new guys really want big, big change,” said one GOP operative who works downtown. “McConnell will not be shocked.”