Try the Multiple Memberships per User add on for PMPro.
It has some limitations. You can only have multiple levels at one checkout when using Stripe. (With other gateways, users will have to do a separate checkout for each level if they are recurring) It doesn’t work with some of the other add ons yet.
Learn how to get it for free here. https://www.paidmembershipspro.com/free/
Here are some other work arounds that work in some cases you would want multiple levels per user. https://www.paidmembershipspro.com/multiple-membership-levels-per-user-pmpro-workarounds/
RE other plugins. WooCommerce Subscriptions probably does it best. I’m pretty sure MemberPress does a lot of work to allow multiple levels per user.
Hope this helps.