Since this is a somewhat semi-frequent feature request, here is a short answer and a somewhat longer-ish explanation:

Yes, it certainly could. Go ask the other mod's author - maybe they'll do it

This mod is designed to store certain stuff (from certain categories and not from other categories ) in certain buildings and not in others.
Like "uncooked food in food basket", "loose goods in skips" etc.

The issues happen when some third party mod creates an entirely new thing which - for absolutely valid and good reasons(!) - may not get categorized under those predefined (vanilla) categories.

Then it's just something that ES does not know and will not store. Period.

We could add this special thing, and that special thing, and oh look, there is another special thing and pretty soon you end up with dozens and dozens of dependencies from ES to all those other mods. Because you better know exactly what that other mod is calling it's stuff. And don't you dare ever change that name or think about disabling one of those dozens and dozens of mods... Because then you get a crapton of errors.
Also... just not enough time...

The other way around would be third party modders adding small patches into their mod which subtly modify ES storage settings allowing and/or disallowing their stuff. That would be much more granular (because each mod only does it's own stuff and ES itself does not get dozens of dependencies)... But now those third party mods need to have a dependency on ES... and why would they want a dependency on some pallet furniture. They add alien space dragons for heavens sake! With laser beam eyes!!! Who cares about storage things!1!111!
Obviously only a somewhat limited group of modders is willing to couple their stuff to ES (because hey, this thing could decide to change things or simply not work anymore - "Thx Tynan").

So... final remark: There is somewhat of a way... for each mod that wants its custom stuff in ES you need an additional "bridge mod". That "bridge mod" depends on both ES and the custom mod and does the mimimal changing of ES's definitions to allow storing custom stuff.
If ES breaks... the custom mod is unaffected. If the custom mod breaks, ES is unaffected.

So ....

You want more stuff in ES: Write those tiny bridge mods . Or find someone who will write them. Modding this game is not that hard and those small glue pieces are probebly some of the easier parts to start with.