Crowdstack has its own built-in premium membership system (called FeePod) that handles all fee collection and automates the granting and removal of premium permissions. However, there is another way to reserve certain features/areas for paying customers, without using FeePod.
The alternative is to use the Crowdstack API (a feature that is not available all plans), along with your own payment system. Here's how it would work:
1. Set up your own payment system using the payment provider of your choice.
You and your provider would be responsible for collecting all revenue associated with your premium plans, but this also gives you maximum flexibility in how you structure your payment plans. As part of this, you'll need to develop or put in place your own ordering pages.
2. Set up your own custom Permission Groups (aka "Circles").
In Crowdstack, set up one or more permission groups ("Circles") to represent your new Premium Membership options. Apply the unique permissions that you wish to reserve for your premium membership (and make sure you do not make those available to the World or All Members).
Side note: you would not want to enable the "Premium Memberships" feature in Crowdstack" because it will assume that you want to use FeePod, and will query people to pay through FeePod, rather than your own system.
Also note that one feature that will not be natively supported if you roll your own premium memberships is the ability to designated specific pieces of content as premium (for instance, a specific blog post, rather than all blog posts).
3. Use the Crowdstack API to manage your premium members.
Your dev team can craft its own management process (via whatever software you have designed to manage your premium system) for ensuring that your Crowdstack member have the proper premium permissions, using the Crowdstack API. Use the API to register new members to your Crowdstack (if necessary), add them to the proper Crowdstack permission group (when they pay), and remove them from the Crowdstack permission group (when they stop paying).
4. Promote your premium membership options on your Crowdstack site.
You'll want to let your Crowdstack members know about the premium options available to them. You can promote this in the header and/or footer Crowdstack, since you have total control of those spaces, with a link to the off-Crowdstack ordering pages you set up in Step #1 above. (Note that Header options may vary depending on your plan.)
The FeePod system that Crowdstack utilizes offers many advantages-- including teasing of premium content, up-selling, and turnkey management-- but if you value control over the collection of payments, then this alternative option may make sense for you.