Unfortunately three males does not work out. The failure rate amongst trios is 90%, there is almost always fights and space is almost irrelevant when it comes to attempting a trio - if the piggies don’t want to be together.
Normally you would look for a suitable pairing - the two piggies who get on best can remain together, and then one needs to be kept alongside but by himself. It does sometimes happen that putting three boys together breaks all bonds meaning none of them can live together. It sounds like that may be the case here. If you cannot find a suitable pairing between them due to them all fighting regardless of the combination, then they will all need to be kept in separate cages and not be allowed back together.
You say one is constantly biting the cage and not settling when he is separated- I am afraid that is to be expected. The instigator of trouble is almost always going to be upset by a separation, but it isn’t his reaction that counts. The two that are calmer are the ones you need to gauge - as they are happier, then it indicates that separation is the best thing.
They can all be kept alongside each other so they can still communicate and interact through the bars. This will ensure nobody gets lonely. Communication is about more than physically being together, so they will be ok like this. However, If you wanted to pair them each up with a new piggy to live with for the long term, then you need to ensure a character compatible match - enlisting the help of a rescue centre to find the perfect companion (going out and buying a piggy runs the risk of a newcomer being rejected and still ending up alone). Each boy can live with one other boy. Equally, they could all be neutered, have a six week wait to become infertile, and then each one can live with a female.
I’ll link in some guides below
A Comprehensive Guide to Guinea Pig Boars
Adding More Guinea Pigs Or Merging Pairs – What Works And What Not?
Boars: Teenage, Bullying, Fighting, Fall-outs And What Next?