The next day is your business.
However, if you shoot with two photographers in the same day, please at least given enough time for the first photographer to finish. Of course that person shouldn't waste your time anyway and planning is best. 

Also, you should know what condition you will be in when you leave the first shoot.  For instance if you do an athletic shoot doing something like skiing, and are too tired to make the next shoot, even the next day, then yes I would be insulted if I was the second photographer and you couldn’t do your part.
Mark

Sorry - Double Post!

not insulting at all!  like many of us have already said, people even set up shoots with 2 or more different photographers in the same day! 

as long as you don't cut a shoot to shoot with another photographer i don't see a problem.  (i have had a model cut a shoot with me at 4am the day of the shoot and try to reschedule for later!!! so she could shoot with a different photographer.  4am!!!!! i had already cleared my day at that time for the shoot.  don't you ever do that to someone.)

if you PAY me i will recommend another photog.

They don't own you....it is not reasonable for them to care if you work with others. If I book you for 4 hours and you show on time, rested enough to shoot and ready to go...I could care less if you just got done working with another shooter, or 5 other shooters.

I would say any photographer that is insulted by that has problems that are beyond your control. I don't see any reason you shouldn't be able to shoot with two different photographers in one day as long as you can be fresh, prepared, and on-time for both shoots.

I'd go with most of the others here, as long as you're not duplicating looks get the work!