I wonder whether there is something grammatically incorrect about the form "to grow," as in "to grow a business," and if so whether it's so commonplace now that it doesn't matter any longer.

If you can grow corn I don't see why you can't grow a business, but there's just no reasoning with some folks.

north: This is a good q and was discussed in some detail at a board I cannot identify for reasons of protocol, but if you are interested I am dalehileman@verizon.net

Welcome, northside. You may be interested in reading what was said here previously (no reason not to add to it here, though):
growing pains

Edit: Hey, it finally dawned on me how to link to a page so that my Search words aren't bolded and italicized!

Bizbabble is like "like, you know" - I can handle it occasionally, but when a sentence contains two or a paragraph three or more of these trendy, obfuscatory, or just plain lazy verbal tics I just tune out. Guess I haven't drunk the Kool-Aid yet. (Bleccccch!)

Despite the fact that they label this a usage problem, I submit that the first definition for the transitive sense in the AHD fits the notion of growing a business better than it fits the notion of growing a tulip. One doesn't cause a tulip to grow, one sets up conditions that allow the tulip to grow of itself.

Even in Brooklyn?

If it's a tulip tree.