Prviate Store + Caching

Hi,

im using WP Super Cache and are very happy with it.
I have a website with a b2b shop that is private, so you need to login to see the products. While debugging i noticed that my private shop plugin (barn2media) disabled chaching for all shop pages. Is there a way to serve Cached Pages in the Private Area to, that and unlogged user cannot see?
I could just disable the donotcache option in the private store plugin, though then i fear that anyone could enter the shop pages, or at least see the content, right?

thank you and best regards
fabian