Note that a customs union amendment was tacked onto last session’s Trade Bill by the Lords: and the Bill then stalled because the Govt feared it didn’t have the votes to strip it off. 
NB also the medicines amendment (passed by both Commons and Lords)
... and the mobility framework amendment passed by the Lords.
Note though that the problem with these amendments is that they can all be repealed after an election by a Johnson majority government, once Brexit has happened.
So if you want a CU/Soft brexit option without a referendum, you are going to have to win the forthcoming election (and you will need the result to land in the zone where “not enough votes for a referendum” and “not enough votes for the deal as it is” overlap).
The calculation for those wanting that option is going to be whether that is best secured by an election now or after the deal goes through.
Though in fact I can’t see that Labour MPs have much choice: whenever a no confidence is put down by Corbyn, they (or at least those standing again) have no real option but to vote for it.
