Just to add to Ty's response, there are a number of factors that work against you making a live recording sound like it's a studio recording.
The very first is that a large part of the sound of a recording can be the room that it's made in. That's why typically recording studios are constructed so that they have "dead" areas, when it is desired to have no sound of the room recorded, and "live" areas, like wooded areas for drum recording. In the studio they have control over things like that. The live recording you have contains the sound of the venue it was recorded in. That sound, the reverb, the acoustics, cannot really be taken out. Manipulated a bit with EQ and gating or downward expansion, maybe, but not completely taken out.
Secondly, studio recordings are normally done either with a lot of isolation between instruments, or done one instrument/voice at a time as overdubs. That way the sound of one instrument does not leak into the microphone set up for another instrument. In live recording, an attempt is often made to close mic instruments, but since everyone is playing together in the same space, there WILL be leakage of sound from all kinds of instruments into mics for other instruments. That limits your ability to EQ just one instrument without affecting the sound of all instruments.
As Ty said, if you have multitracks of the live recording, you may be able to EQ the individual instruments or voices to improve their quality, but you still will have leakage and room ambience in there. Not to mention the sounds of the audience.
So you might be able to improve on the live recording, but it's still going to sound like a live recording more than a studio recording.
When you make coffee or tea, you might add milk or sugar. Once you add it, it's there to stay. Any recording is the same way - whatever environmental noises are captured are there to stay. There are destructive ways of removing them (no matter how advanced the tecnique, you still have to make compromises on quality).
I, for one, very much enjoy live recordings of any sort and feel that they bring a different dimension to the recording that can't be found in any studio. I think it would be best to live with what you have, so long as it is a quality recording - or at least of a quality that you are pleased with.