It depends a lot on how flexible your “basic functionality” is and how flexible you are in it.
Particular suspicions in open source CMS systems come to mind if your application mainly requires standard features, and you can create modules for it to suit your specific requirements. If you cannot find what works for you, you go into the programming framework and develop it yourself.
You need to decide how many components you want to keep "in the house." You can transfer the bulk of the core functions of your websites (if you decide to do this). I like Amazon DevPay for credit card processing, and to process your account, you can check the login capabilities using the stack.
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