Can a seller carve out a side business they already run before agreeing to a non-compete?

Yes, and this is both a sensible and commonly used approach. A non-compete can, and generally should, expressly exclude a specific existing business or activity that the seller already runs and disclosed before signing, so the covenant is understood from the outset as not reaching that named, pre-existing operation, rather than leaving the seller to argue later that it was somehow implicitly outside the scope of a broadly worded clause.

Building in this kind of carve-out also supports the enforceability of the rest of the covenant, since a restriction targeted precisely at protecting the goodwill the buyer is actually purchasing, without unnecessarily sweeping in an unrelated activity the seller was already engaged in beforehand, is more likely to be seen as reasonable if it is ever challenged. A seller with an existing side business should raise it explicitly during negotiation and make sure the carve-out is written into the non-compete clause itself, rather than relying on an informal understanding with the buyer that never makes it into the signed agreement.