Partial Content is supported only for the requests for reading from the cache. Files loaded not completely do not remain in the cache.
If you have time, maybe you could consider to get some referrences of Partial Contents Caching from Varnish Cache.
This is the URL of Varnish Cache :
https://www.varnish-cache.orgIt really work on BSD Family (I have tested it) and also works well on Web Server (server side) and Local Server (Client Side).
Please be carefull when you reverse it since (for me) it's not easy to reverse caching between server side and client side.
Disclaimer
I'm not Varnish Cache staff.
I just happy user of it.