The GOP presidential field is now, officially, thicker with senators than at any time in the past two decades. All three with declared candidacies have viable paths to the nomination — underscoring the bewilderment about why a fourth Senate Republican, who would be among the longest of long shots, is considering joining the hunt.

South Carolina’s Lindsey Graham does not have an obvious niche to fill in the primary field, or even a viable way of marketing himself as unique among the other senators already in the race. Yes, he’s more of an internationalist and a bigger defense hawk than either Rand Paul of Kentucky or Ted Cruz of Texas. But his muscularity is only marginally more aggressive than the posture of Florida’s Marco Rubio, who announced his White House bid Monday promising a presidency in which “America accepts the mantle of global leadership,” both diplomatically and militarily.

If Graham stands out in any way, in fact, it’s as the sort of deal-making and ideologically iconoclastic congressional Republican viewed with either suspicion or derision by most important factions of the party base.

Although he and Rubio both promoted the 2013 immigration overhaul, Graham has stood apart from all three GOP senators running for president in backing federal intervention to reduce global warming, deficit reduction partly with higher taxes and the confirmation of Loretta Lynch as attorney general.

And yet he’s been in testing-the-waters mode in the five months since winning his third Senate term — working on the weekends to introduce himself to voters in Iowa and New Hampshire and stopping by cities and well-heeled suburbs along the way to raise money for his brand-new Security Through Strength political action committee. If the results on both fronts seem promising enough to him, he’ll formally announce his candidacy before Memorial Day.

There are two equally plausible reasons he’s taken things even this far, and they are not mutually exclusive.

Maybe he’s volunteering to be a vessel for the frustrated national ambitions of his mentor in maverick behavior, senatorial best buddy and partner in pungent humor and saber-rattling — John McCain of Arizona.

Or maybe he’s hoping to revive the lost role in presidential politics of the favorite son and kingmaker from a vitally important state.

Either way, at this point it’s reasonable to expect Graham will end up relegated to a more familiar, but unwelcome part in modern GOP presidential campaigns: the influential member of Congress whose ambitions and legislative accomplishments get recognized hardly at all by the voters. (The designated congressional asterisk was played in 2000 by Orrin G. Hatch of Utah, then the Senate Judiciary chairman, and in 2008 by Rep. Duncan Hunter of California, fresh off four years as House Armed Services chairman; each dropped out after drawing less than 1 percent of the vote and bringing up the rear in the first two nominating contests.)

Gauging Graham’s nationwide level of support has been impossible because he’s not even being listed among the dozen or so Republican names included in most national or early-state polls.

This has included, until recently, the polls in his native South Carolina, although two recent surveys placed Graham in a statistical three-way tie with former Florida Gov. Jeb Bush and Wisconsin Gov. Scott Walker. At the same time, the highly respected Winthrop Poll last month found 57 percent of Palmetto State Republicans opposed to their senior senator running for president.

That suggests a decent but not impossible climb, if all Graham really wants is more affirmation from his own people. But he’d probably not put his grass-roots organization and fundraising ability on the line for such a shallow objective. More likely, he’d run to retain control over his state’s big money and GOP power structure, freezing their movement toward any other candidate.

That way, his eventual endorsement of a more viable rival could deliver unusually big benefits — to his chosen candidate at a pivotal point in the campaign, and to Graham himself after that. (He’ll turn 61 next year while completing 14 years in the Senate. And with a prominent full committee chairmanship at least six years in his future, it’s easy to imagine Graham wanting in 2017 to become the first colonel in the Air Force Reserve who’s promoted to secretary of Defense.)

South Carolina, of course, is not just any other state on the GOP calendar. It’s likely to have the second primary next winter, and the party powers are eager to revive the state’s record of going with the eventual nominee. (That happened in all five contested primaries between 1980 and 2008; but last time, in 2012, former Speaker Newt Gingrich, R-Ga., upset Mitt Romney.)

While neutralizing the other aspirants on his own turf, a candidate Graham would guarantee the presence of a provocative voice from the GOP’s interventionist wing. And if primary voters of a certain age here brings echoes of a different era, when an assertive view of the nation’s role in the world was the default setting for party leaders, that’s just what the 2008 GOP nominee and 2000 runner-up had in mind.

McCain, who may be the only Republican senator even more passionately disapproving of the Paul and Cruz approach to foreign policy than his running buddy, has been talking up a Graham candidacy almost as much as Graham has.

During last week’s recess, Graham spent part of a day as the guest of one of his other closest comrades in the Senate — Kelly Ayotte of all-important New Hampshire, although they chose not to spend their time in her backyard talking up their shared hawkishness. Instead, they visited a plant that makes airline ball bearings for Boeing, a main beneficiary of Export-Import Bank of the United States loan guarantees, to profess their shared support for reauthorizing the bank as a worthy U.S. tool of global economic growth.

Paul, Rubio and Cruz all want to shutter the bank, which they lambaste for providing “corporate welfare” with taxpayer backing.

If Graham can run a credible campaign on distinctions like that, he’ll be defying every available assumption about the 2016 GOP field.

Correction April 16, 6:20 p.m.

Due to a typo, a previous version of this story misstated the year in which the next presidential election takes place. It is 2016.

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