The vote is not a rerun of the Jan. 15 vote on whether to approve the exit deal she had negotiated with the European Union, which she lost by 432 to 202.
If May can't break the deadlock, Britain will leave the world's biggest trading bloc without a deal on March 29. In the event of a chaotic "no-deal" Brexit, the Bank of England has warned the country's economy could shrink by as much as 8 percent in about a year.
On Tuesday, May is forcing lawmakers to show their cards on what sort of Brexit, if any, they want. It is a chance to discover what sort of changes to her strategy would be required to win the support of Parliament, so May can try to renegotiate the deal in Brussels and then ask lawmakers to approve it.
May has said she wants to secure concessions relating to the border with Northern Ireland in order to win the support of pro-Brexit lawmakers in her own party and the small Northern Irish party which props up her government, who voted against her deal.
Some lawmakers want to shift control of the process away from government and give Parliament the chance to define Brexit. If successful, this could have a profound effect, giving lawmakers who want to block, delay or renegotiate Brexit a possible legal route to do so.
Other lawmakers have proposed alternatives to May's deal to gauge support for them and persuade the prime minister to change course by seeking closer E.U. ties or holding another referendum.
Lawmakers have proposed more than 10 different amendments to be debated on Tuesday but only a small number are likely to be chosen to be voted on. Voting will begin at 7 p.m. local time (2 p.m. ET).
If a subsequent piece of legislation is passed, it would give May until Feb. 26 to get a deal approved by Parliament or face a vote on whether to ask the E.U. to delay Britain's departure.