Solomonski means "son of Solomon", starting with the Hebrew root for Solomon.  The German root version is Zalomon.  The Yiddish alternative to Solomon/Zalomon would be Shloyme or Shlomo, derived from 2 Samuel 5:14.   If your ancestor had a conventional Russian connection, the name might have been Solomonovich.  The According to Beider's surname dictionary, there are over 100 variants that are based on these primary roots.  Although Solomonski as spelled is not common, that is because it is one of many potential variants of the same basic surname.  Therefore, you were wise to wonder how many variations there are.  The answer is...many.

It is safe to exclude Slonimsky as a variant spelling.  Two of my ancestors came from 30 miles away, so I immediately recognized Slonimsky as being associated with Slonim, a town in present-day Belarus.  Solomonski and Slonimski have somewhat similar spellings, but they are completely different surnames, with one derived from a person, the other derived from a place.  Beider's dictionary also recognizes that distinction.

Hope this helps.   Good luck in your search.

Ken Domeshek
Houston

Damesek, Braverman in Nesvizh
Kartusinsky, Sinienski, Stasinsky in Nowogrudek, Korelitz, Lyubcha, Negnewicze, Rutitsa.