The Republican National Committee (RNC) sets out in its Rule 9 the terms for "filling vacancies in nominations".
It reads: "The Republican National Committee is hereby authorized and empowered to fill any and all vacancies which may occur by reason of death, declination, or otherwise of the Republican candidate for President of the United States."
Death may be off the agenda, so what about the other scenarios?
Mr Trump would voluntarily leave the race.
With "Rule 9" invoked, the RNC could then either reconvene the 2,472-delegate convention to vote again - a virtual impossibility at this stage - or the board of the RNC, with 160 members representing all states and territories, would select a replacement.
Each state and territory would have the same amount of voting power that it had at the convention. Mike Pence, the vice-presidential nominee, would not get an automatic promotion because the board could choose anyone to fill the vacancy.
Many Republican representatives and senators would welcome a new candidate as he or she could help them hold on to their seats.
Unfortunately for Trump opponents, the candidate has shown no intention of exiting the scene. His comments after the latest obscene remarks controversy - "See you at the debate on Sunday."
The anti-Trumpers might take some comfort in the vagueness of the phrase.
Rule 9 has never actually been used before and so its boundaries have never been tested. The last time a candidate left the ticket late was in 1972. Democratic vice-presidential candidate Thomas Eagleton was forced off after his bouts of depression were made public.
"Otherwise" is generally taken to cover the gap between death and declination, perhaps a coma or stroke or other illness that leaves the candidate alive but unable to signal withdrawal.
As such, it is about filling vacancies and not creating them.
But some have suggested a broader interpretation, taking "otherwise" into areas such as acts of criminality, treason or even adopting principles "fundamentally at variance with party principles", as commentator Thomas Balch puts it.
But Mr Trump could sue if the "otherwise" path were taken against him.
By the way, even if he did commit a criminal act, it would not bar him from running for the presidency. He could possibly pardon himself after winning.
Rewriting the rules
Time has run out, it would seem, even if there were the inclination.
Rule 9 can be amended by a majority vote of the RNC's Standing Committee on Rules, followed by a three-quarter majority in the RNC. But it would only take effect 30 days later.
The voting problem
Tens of thousands of Republicans have already cast their absentee votes, many of them in the key states of Florida and North Carolina. What happens to them?
Many state set deadlines locking the names on ballot papers so that electoral procedures can run smoothly. Those ballots now have Mr Trump's name on them, and the deadlines have passed. Anyone voting for a Republican candidate would probably have to select Mr Trump.
This happened in Florida in 2006, when representative Mark Foley resigned five weeks before polling day. The Republican Party failed to get replacement Joe Negron on the ballot. Its "punch Foley for Joe" campaign failed to retain what had been a safe Republican seat.
Vote for someone else
Without Mr Trump leaving the race, a Republican replacement isn't possible under the rules.
Libertarian presidential candidate Gary Johnson is a former Republican and served as the governor of New Mexico from 1995 to 2003. He did pull in 1.275 million votes in 2012 and is on the ballot in all 50 states.
Evan McMullin, a former CIA agent and Republican Congressional staff member, is also running as an independent, but he entered the race too late to compete in every state.
The downside for conservatives is a third-party vote could aid a victory for Democratic candidate Hillary Clinton.
The Green Party's Jill Stein probably won't attract many Republicans.
Denounce him and sit this one out
"Better luck next time" isn't the most comforting election strategy, but some disaffected Republicans think their best option is to denounce him and wait. More and more are signing letters and writing columns denouncing Mr Trump.
Thirty former Republican lawmakers did that on 6 October, saying in a letter that Mr Trump lacked the "intelligence" and temperament to be president. They didn't propose any removal, just that voters reject him at the ballot box.
Hope he wins and pick up the pieces
Mr Trump has been underestimated before and eventually came out on top. Republicans have made it this far enduring Mr Trump's wild campaign, so what's another month?
The executive branch is a huge undertaking involving thousands of positions and there aren't enough Trump loyalists to fill them all. Republicans - even ones uneasy with Mr Trump - will be able to shape policy and deliver on issues important to their constituents for the next four years.
On the other hand, Mr Trump may have done lasting damage to the Republican Party's brand with Latino, black, Muslim and women voters.