Not~but~ construction

As others have said, off the couch is not really idiomatic, but for example under the couch would be, so I will take your sentence to be

Someone is lying not on but under the couch.

This type of coordination construction, which is not special to the coordination of preposition phrases, is usually called 'right node raising' (RNR), though CGEL prefers to call it 'delayed right constituent coordination'.

Using basic coordination, your sentence would read

Someone is lying not on the couch but under it.

Discussion

RNR is famous in linguistics because it 'is a phenomenon that challenges theories of syntax in significant ways.' CGEL introduces it as follows (p. 1343):

In this construction the constituent which in basic coordination would appear as the rightmost element of the first coordinate is held back until after the final coordinate:

[21]  i  She knew of my other work but never mentioned it.               [basic coordination]
        ii  She knew of but never mentioned my other work.       [delayed right constituent]

In general, the effect is to heighten the contrast between the coordinates by removing from them material that would be the same in each. But the construction is appreciably more difficult to process than basic coordination, both for the addressee, who has to hold the first coordinate in mind until the sense is completed at the end, and for the speaker, who has to plan ahead to ensure that each coordinate ends in a way that syntactically allows completion by the delayed element - as knew of and never mentioned both allow completion by an NP complement.⁶⁶ Characteristically, there is a prosodic break after the final coordinate, signalling that the element that follows relates to the whole coordination, not just to the final coordinate.

^{66Examples are found where this condition is not satisfied. One case is illustrated in ?I always have and always will value her advice, where the plain form value is an admissible continuation of will but not of have: compare basic I have always valued her advice and always will value it. Another involves coordination of comparisons of equality and inequality: ?It's as good or better than the official version, where as good takes a complement headed by as not than. Such examples are not fully grammatical and would generally be avoided in monitored speech and writing; the second can be corrected to It's as good as or better than the official version.}

In your case, the constituent that is 'held back' is the noun phrase the couch.