From the offset, I'm not a big fan of using modals for multiple step forms; since you will inevitably have to "stack" modals, or similar components, on top of it for semantic (success, warning, error) messages during the filling out process.
Maybe offering access to that multiple-step form from inside the original page is a more straightforward option:
"Do thing" button at relevant page
"new" page with step 1 of doing thing with a "back" or "cancel" button (that takes you back to "relevant page") and a "next step" button
Step 2, 3, 4... with a "previous step" and "next step" buttons
Final step, where you check the submitted info and confirm (which sends you back to "relevant page"), or go to previous step.
If you have a lot of (well defined) steps, a widget that allows you to jump to any step you want might be handy.
In any case, I don't believe a modal is the component to be used here. Move the user to a "deeper" level (like "List of things page" to a "Create new thing page") and avoid awkward interactions like modals popping up with the back button, and free the modal component to be used in things like "you're gonna lose the info behind this modal if you leave" warnings and such.