LONDON — Ahead of a vote on her Brexit plan that could go down to a humiliating defeat in Parliament, Prime Minister Theresa May of Britain was fighting on Monday less to avert the loss than to limit its scale.

In that vein, Mrs. May enlisted fresh promises from Europe’s most senior officials through an exchange of letters and warned supporters of Britain’s withdrawal from the European Union that the whole project would be threatened if her deal was voted down as expected.

Neither tactic looked likely to change the overall outcome, but if Mrs. May can curb the magnitude of any defeat to manageable proportions, she could avert an immediate political meltdown. That, given the precarious state of events, would be a victory of sorts.

[What is Brexit? A simple guide to why it matters and what happens next.]

Speaking in a ceramics factory in Stoke-on-Trent, an area that voted heavily to leave the European Union, Mrs. May warned that Britain’s failure to withdraw from the bloc would risk “a subversion of the democratic process” and do “catastrophic harm” to faith in politics.