In addition to choosing a light OD that fills out the sound and makes it more harmonically dense, the right type of compression and EQ may be beneficial.
However, trying to do too much with the bass will likely muddy things up or drastically change the bass tone in a way that is not style appropriate. For example: Reverb adds space, but typically does not work well on bass; especially in a live environment. The exception of course is if the music is atmospheric, which I am guessing it is not. Adding modulation effects like chorus or flanging can fill up some space and sound cool, but are these types of tone within the style you are covering? If you don't care about how closely the performance resembles the original recordings, you can do whatever you want and it can potentially sound very cool and artistic, but the audience may not understand or appreciate it.
IMHO a better approach is to choose tunes that work with the group format. If everything sounds fine until the guitar player starts to solo, the choice of music and/or the way the guitarist plays is the actual problem. So, usually the guitar player is the one who actually needs to fill out most of the space and this changes the nature of their solos: notes, how they are played, and the effects used.
I suggest listening to recordings of groups you think pull it off well.