I think the simple answer is you institute 135 regs. Of course, there are all kinds of hybrid and in-between variations if you want to get complicated. But basically, if you're Part 91 and feel you are flying so much that you need some guidance on duty/flight times, then use 135.
I guess the difficult thing here becomes the question of "pop-up" flights. But there's no generic answer to that question. It depends on the flight department, their habits, the number of airplanes and so on. Yea, you might have to make yourself available 24/7.
Wow.. what a tough job we have!