Most of the opposition parties are in favour of leaving the EU but joining EFTA and possibly a customs union with the EU (crossing Theresa May's 'red lines'). Are there enough Conservative MPs also in favour of this 'softer' brexit to command a majority in the Commons?
The reason it cannot get a majority in the house is simply that it's not being put before them for them to vote on it. There is only 'This Deal or No Deal' (according to the government, who control the business of the house)
One of the amendments to the vote to delay Article 50 (amendment i) was trying to put mechanisms in place for this consensus/compromise deal to be defined, debated and voted upon, but that amendment failed.
Parliament voted by a majority of only 4 votes to rule out a no-deal Brexit. Which tells me that surely something only a little bit softer than no-deal could win a majority, if it were put to the house.