I’d agree with Peter - start by breaking up the Minimee calls to give you lots of little minimee downloads: depending on how much stuff you have, maybe even try doing one per item to begin with. Once you have done this, you can exploit the queue / display
feature to stack up more than one entry to see how combinging them works. For example:
{exp:minimee:css queue="header”}
… css stuff …
{/exp:minimee:css}
…other stuff…
{exp:minimee:css queue="header”}
… more css stuff …
{/exp:minimee:css}
… other stuff …
{exp:minimee:display css="header”}
will give you a single block of minimsed CSS cached by minimee that combines the two ‘header’ queues entries.
Useful documentation here - http://johndwells.github.io/Minimee/
HTH