Towing with a company truck?

There may be bylaws in the company that prohibit or limit it. If it's a small business, probably not; but if it's a family business that has been around for more than one generation, an incorporated business, or such, then there might be bylaws that limit stuff like that.

I use my commercial truck to tow for personal purposes sometimes. My truck has USDOT numbers and company name and logo, as per DOT regulations. When I tow for personal purposes, I cover up my DOT numbers with magnetic 'not for hire' signs. This signifies that I am not conducting business on this trip.

On the insurance issue, commercial trucks are required to carry so much more insurance than personal vehicles, that I would rather have an accident in the commercial truck, if someone wants to really try to sue the pants off me, since I have double the liability limit on the commercial truck than I do on my personal vehicles. Because of the business, I also have an umbrella liability policy, so I'm double covered with that.

What Turtle said...and insurance might not cover any accident...your personal and/or
the company's insurance...

If the GVWR of the truck is over 10,001+ lbs AND you use it commercially, you are required to comply with the logbook, some vehicle licensing, and other laws. Many states assume that it is commercial if it has signage on it. In some all you need is a ladder rack or something similar, and you are deemed commercial. A friend of mine got busted bad in Iowa for logbook requirements, all he had was an F-350 with magnetic signs on the doors, hauling his motorcycles back from Sturgis. He went past a scale and one of the creeper cops chased him down.

If the GVWR is 26,001+, then a whole set of laws start applying (CDL, etc).

I see people do this all the time. Yes, there could be liability issues for insurance. And in the event something bad happens, perhaps there could be civil liabilities. But there is nothing illegal about it.

Non that I know of.

But it could be a problem if the truck has DOT numbers on the side for your company or business. All trucks for hire and that have DOT numbers on the side have to stop at scales.

This "may" put you in a bad place?

Not that I know of.
However, I could for see liability and insurance issues in the event of an accident particularly if you were at fault.