According to this article [
theramswire.usatoday.com] the Rams are in line for one 4th round comp pick (JJ) and three 6ths (Ebu, Everett, and Fox).
Hopefully Reynolds and Jackson cancel each other out so the Jackson signing doesn't cost the Rams a comp pick.
The Rams will probably sign Blythe at some point. Other than that I don't see the Rams signing anyone else before the draft. (And even if Blythe signs somewhere else I doubt it would affect the Rams' comp picks: he wouldn't get the Rams more than a 6th for sure, and the Rams can't have more than 4 comp picks.)
AlbaNY_Ram