Unfortunately, Stripe user guidelines only allows Administrators to connect to 3rd party applications like Payment for Stripe. Therefore, if you would like to have several employees or volunteers using the app under different user accounts, you'd have to grant each user an Administrator account.
However, Payment Enterprise allows for more granular control of your users within the apps. By enrolling in an Enterprise account, you can add "charge-only" users; users that cannot log in to your Stripe account, nor see any previous customer or payment data in the apps. The only role for them would be to process transactions on behalf of your Stripe account.