Hello Shaz and Tony,
Welcome to our forum.
If you are looking for something more than just a physical hook-up, then you're talking about polyamory, and as such, this should be a good site for you.
This new partner Shaz seeks, would it be acceptable if they had another partner of their own? If so, they would probably be okay with just getting together with Shaz occasionally.
Links to try to look for poly people in your area:
Feel free to look around on this site and ask questions, etc. ... I wish you well in your poly search.