All this talk about IP's and you people are heading in the wrong direction. The issue isn't with IP's but with Browser capability. Pinterest is a browser-driven app. In Chrome, you can set up more than one account (click: Manage People, under account settings). Set up a separate Chrome browser profile, one for each of your Pinterest accounts. Separate cookies will be saved for each browser account. If you want Pinterest #1, switch Chrome account to Person #1. If you want Pinterest #2, switch to Chrome account #2, etc.
These articles will solve your issue:
lovelyblogacademy [dot] com/manage-multiple-pinterest-accounts/
support [dot] google [dot] com/chrome/answer/2364824?hl=en-GB