Is it possible to customize multi-touch gestures on an iPad?

The iPad has multi-touch gestures:

Is it possible to customize these gestures? If so, how?

Not out of the box - the closest you could get some gestures is to jailbreak and install Activator which allows you to e.g. customize pinch and spread actions, slide from left/right/bottom/top of screen and then assign and action e.g. launch an app, lock the screen etc.

If you're talking about customizing the way you invoke these gestures, I think your only option (without jail-breaking) is to make it so that instead of having to perform these gestures, you tap a few buttons. Apple calls this feature AssistiveTouch.

For example, if you want to exit an app by using AssistiveTouch rather than performing the normal gesture, do both of the following:

To create a new gesture (do this one time for each gesture):

1. Launch Settings
2. Go to General
3. Temporarily disable the multi-tasking gestures (this will make it easier to record the gesture)
4. Navigate to Accessibility > Assistive Touch
5. Enable it on the top
6. Create a new gesture
7. Perform the close app gesture (start with four fingers spread out, and then slide all four fingers towards the center).
8. Press Save on the top right, and name it something like Close App.
9. Re-enable multi-tasking gestures (Settings > General)

To use the gesture:

1. Make sure you are in an app and not looking at the home screen.
2. Tap the new transparent button which appears on the bottom right.
3. Tap Favorites > Close App.
4. Tap in the center of the screen
5. You should now see your home screen instead of the original app you were in.

It's not that practical, since you end up having to tap 4 buttons instead of performing a single four-finger gesture, but it's an option in case anyone needs it.

Tip: if you don't want the AssistiveTouch button always visible, in the Accessibility page, you can set it to appear and disappear by triple-tapping the home button.