Change dedicated IP on multisite network

Hello.

While my customer base has been growing, my site is now starting to load very slow (including all other sites on my network), especially in the backend. I’ve been talking to my hosting partners and my PHP memory are fully used, so the solution looks like i need a better server, with more memory.. If i change the server i will be given a new dedicated IP – how will that affect my network? I have a couple of customers with DNS domain redirection, so i have to change it there of course, but will it affect it in other ways?

Best Regards,

Rasmus