The government has urged pro-EU Conservative MPs to "work with us" as it seeks to avoid a Commons defeat on post-Brexit customs.
Several Tories have expressed support for a call for the UK to stay in a customs union if there is no trade agreement by 21 January 2019.
The government says joining a customs union would prevent it from striking trade deals with other countries.
MPs have started voting on suggested changes to the Trade Bill.
The government has already lost one vote, with MPs backing an amendment that would keep the UK in the European medicines regulatory network.
MPs are now voting on the customs union amendment tabled by pro-EU Stephen Hammond.
Mr Hammond said his amendment was "exactly in line" with the negotiating position set out by the government last week.
It supports the government's aim of negotiating a free trade area for goods but states if this has not happened by 21 January, ministers must change tack and start discussions on joining a customs union.
Trying to avoid a rebellion, International Trade Minister George Hollingbery offered to make new changes to the bill when it reaches the House of Lords.
"Let's do this the other way round," Mr Hammond replied, urging the government to accept his amendment instead.
The motion on joining a customs union is being backed by Labour, making the risk of defeat more likely.
PM 'caving in'
The UK is due to leave the EU on 29 March 2019 but has yet to agree how its final relationship with the bloc will work.
The government, which does not have a Commons majority, has been under pressure from MPs on both sides of the Brexit debate.
The Trade Bill would create new structures for dealing with trade disputes after Brexit and carry over up to 40 existing EU trade agreements with other countries that the UK wishes to stick with until new deals are struck.
The government twice survived by just three votes on Monday after a backlash from pro-European Tories who accused the prime minister of "caving in" to the party's Eurosceptic MPs.