No, there should be no issues running multiple multisite installs in a single VVV setup. I have at least 4 multisite installations running on my machine as I type this.
Your issue is likely either because your multi-sites are identical, and share database tables and/or URLs, or, you’ve added a subdomain site and you now need to re-provision VVV to get the new subdomain in your HOST file and in NGINX.
Try running this from the command line:
vagrant halt; vagrant up --provision
And make sure that your 2 installs have separate tables/database names/URLs. A VVV set up will give you a standard server stack with Nginx, for which there is nothing special other than how it’s provisioned.