My place has a rule against this. My last place fired someone, mid-term, for doing this. And we haven't offered $38K for a tt job to a social scientist holding a PhD in 10 years, and we're in flyover country.
I'm in Florida; we set the bar for low-balling new TT hires ($40,000/year, 4/4 load at some of the private colleges out here. It's not pretty).
To the OP, yes, check with your college/uni first. Some places allow it as long as it doesn't "interfere" with your duties, but, as someone on the tenure track, I don't see how you'll have time for this while still being able to keep up with your main duties (i.e. teaching, research, publishing, committees, etc, etc).