It's possible to create multiple signup forms if you build your own using the custom signup form. It's not possible to customize the default signup modal to collect different profile info for each membership.
Memberstack gives you the ability to build as many signup forms as you like as well as picking & selecting the custom fields you include for each of those (email and passwords are required fields).
Just be aware that Memberstack can only help you test one signup page at a time — as shown below.
Note: Each custom form will need to go on a separate page.