Is there any way to make an ionic modal have a ui router nested state with multiple modal pages?
It sounds like you are describing a wizard, A model that has multiple pages (or steps). Because Ionic and AngularJS go hand in hand with each other you can use some of the pre-built AngularJS components to achieve this, here is a link to a few:
I would recommend not doing that because I have tried it in the past and in the end I realized that it wasn't really practical. What you could do is, add:
ng-include src="'your-template.html'" ng-controller="yourTemplateController">
Now you have a view and a controller associated with it. All that is left to is, make the url change. This can be done by using location.hash, or setting $stateParams and checking for it using $watch. I hope this helps.