Can you interactively modify the terminal reset in 'less'?

I usually do not want to reset the terminal when I exit less (that is, I want the screen to continue displaying what I was looking at). Usually, when I'm on a new box and haven't configured it yet, I invoke less, quit, see the screen reset, curse mildly, and rerun with less -X ... On very rare occasions, I remember that the screen is going to reset as soon as I quit, in which case the sequence of events is slightly modified and the mild cursing occurs before I quit, but the overall effect is about the same. Is there any way to modify a currently running less process so that it will not reset the terminal upon exit?