Knowing that PROS implies "being with" or "toward" or even in proximate communion with someone else, certain theologians have tried to explain Jn 1:1b-c by resorting to a priori categories of person and substance. However, John McKenzie has pointed out that John did not differentiate between the divine substance and divine Persons who are identical with the divine substance. John simply used QEOS to describe the Being he identified as the only true God (John 17:3). This Being is distinct from the man who was called Jesus Christ on earth, and He is also set apart from the LOGOS who was with the only true God before the world was (John 17:5).
The problem that has not been satisfactorily addressed by Trinitarian theology accordingly involves in what sense the Son and Spirit are Persons. To be sure, theologians have endeavored to cut the Gordian knot of this troublesome antinomy. Nevertheless, not one thinker has satisfactorily explained how Persons who are not Persons in the Cartesian sense (COGITO ERGO SUM) can subsist with (PROS) one another
and enjoy meaningful communion or love one another.
G. R. B. Murray says that PROS TON QEON (Jn 1:1b) means: "in the presence of God" or "in the fellowship of God." He probably is suggesting that God the Son communed with God the Father. B.M Newman and E.A. Nida reject the "in the presence of God" understanding for this construction and opt for the notion of "a kind of interactive reciprocality between the Word and God."
None of these explanations make sense to me within the context of a non-social Trinity doctrine. Of course, if one posits a social Trinity, then tritheism must be avoided or the idea that there are three "I thinks" within God. Trinitarians, please don't multiply antinomies beyond necessity. With apologies to Ockham!