How do I set a key frame between 2 frames? The reason I want to do this is because I want to render in different frame rates without needing to change every time and some objects start and stop between frames. Do I have to scale everything up by increasing the frame distance between key frames, change the output framerate scaling and finding the lowest common denominator?
I don't think that's possible.
What you can do, however, is scale your entire animation to create more frames in between the existing ones.
Enter the graph view and move the time cursor to 0. Then select everything and press . (to scale relative to the cursor) followed by S X 2 to scale by a factor of 2 in the X direction (i.e., along the time axis).
You can then adjust the project's frame rate, modify the frame steps (in this case double it) and etc. to get it playing at the right speed.