I feel your pain, brother, because I had the same problem. I always got my rhythm sound from the amp and/or a stomp box. Typically I wanted my solo to have the same tonal characteristics, but just be louder. A lot of pedals either color the sound, don't raise the volume level enough, or make your leads sound thin and wimpy.
In about 1995, one of magazines published a pedal roundup. Surprising, I don't think it was a guitar mag but one of the recording magazines (Electronic Musician, Recording, EQ, etc.). Anyway, one of the pedals they mentioned was the Rocktron Austin Gold. It has three knobs: Level, Drive and Pre-bass. I forget the exact spec, but the Level knob adds like 15 or 18 dbs without coloration. The Drive knob is very, very, very subtle and will add just a little hair. The Pre-bass knob adds to the low end of your tone, which can frequently be robbed, to put a little meat on the bone.
Of course, a little delay can help, but if you are already running a delay while playing rhythm then you might be out of options.
The Rocktron Austin Gold is a very under-appreciated pedal. It is always in my signal chain, no matter what rig I am using.
The goal is soul. May the Force be with you.