Can I have multiple memberships on same site?

Ok, I think we may have discussed this some months back, prior to the current version of Membership (3.4.4), but now can't recall if doable...

I would like to have "parallel" memberships hosted on the same site (aggregate all the traffic in one place for one). A user may be a member of one or more sites - with the goal that they sign up for one membership but then cross-sell to another.

So, user ideally could be in two or more memberships simultaneously.

Of course membership lets you set this up - how do you go about setting up the access levels so that it all works as it should - if I am in just one membership, I only see that content - if I opt in to another membership, I now see both sets of content, and if I am just a visitor - I see nothing...

Making any sense? How to manage...