I have a $99 (on-sale) Harbor Freight 10 gallon compressor that I have
been really satisfied with for my home-hobbyist use -- it has more than
paid for itself many times over.

I was wondering though whether I could effectively increase its capacity
(at least for short intervals) by attaching one or more 5 or 10 gallon
portable tanks to it.
Would this give it the *effective* capacity of a larger tank allowing me
to have a longer burst capacity? (though filling the combined tanks
would obviously take longer)

Any issues with doing so?