I understand that a coordinating conjunction must combine two words, phrases or clauses of equal weightage, thus, a coordinating conjunction must never combine a clause and a phrase. It should be either a word-word relationship or a phrase-phrase one or a clause-clause one. What role is the coordinating conjunction 'but' playing in this sentence then -
I would like to watch a movie but not alone.
I believe that but in this sentence is combining a clause (I would like to watch a movie) with a phrase (not alone). Can someone clarify if I am making a mistake in identifying the role of but here?