I think it is OK to let the new bunny exercise in spaces that your other rabbit exercises in, as long as your other bun isn’t there!
Your original bun might show an uptick in marking, but other than that I think he will be OK.
The only thing that would really harm bonding is if they fought, so just be sure they cannot access each other (even to nip noses through a fence). Rabbits are VERY persistent at getting at “intruders”, and will surprise you at how high they will suddenly jump over a fence they’ve never bothered to jump before!
A couple weeks post-neuter you can start up “pre-bonding”, where it’s actually encouraged to let the buns see and smell each other, and to swap cages or litter boxes so they start to really lose track of their territory and get used to the other rabbit’s scent. Waiting till after new bun’s neuter will help him settle in, and his hormones will change the way he smells after he’s neutered.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.