How to have multiple independent subscription-level's?

I want to have multiple independent subscription-level's that people can sign up for one, some, or all of them.

Every time I make more than one subscription-level "public" it treats them like "upgrades" where signing up drops the level the person was on and replaces it with the new subscription. I don't want one to be dropped and replaced with the new one. I want them to have TWO (or more) subscription-levels.

Making the subscription private and manually creating a subscription button with short codes seems to do nothing (it just returns to the subscription page having changed nothing).

Right now all subscriptions are "serial, 365" Options>limit upgrades=365. I have only one subscription as 'public' at this point.