It depends on what browser and operative system you're using.
Firefox lets you increase the max quota. Open the page
about:config
, search for the string
dom.storage.default_quota
and edit its value. It's expressed in kilobytes, so 5120 kB = 5 MiB
Iirc Chrome-based browsers (including Edge, Vivaldi and Opera) don't let you store more data. An alternative is
FCHost: it's basically Chrome, without cache limits. It has been developed to play
Free Cities, but it should work with any HTML game. More info
You must be registered to see the links
.
Saving on your hard disk is still your best option though.