Are you able to be on burst mode while shooting in self timer mode with the 5dii? I'd like to be able to take more than one shot at a time while being on self timer.
No, it is not possible. That is because to use the self timer you must select one of the two Self-timer drive modes. To shoot bursts you must select the Continuous drive mode. You may only select one drive mode at a time, so you must choose one or the other. The same is true with a wireless remote, since that also requires using one of the Self-timer drive modes.
One workaround you have is to use a wired remote with a built in intervalometer such as the Canon TC-80N3 or generic equivalent. Plugging a wired remote into the N3 port allows you to use the camera in any drive mode, since the wired remote functions exactly as pressing the physical shutter button. You could set the timer in the wired remote to have a 10 second (or 10 minute, or whatever time you choose) delay before activating the shutter. If the camera is set to Continuous drive mode and set to a specific shutter speed, semiautomatic, or auto mode you can set the set the timer to hold the shutter open for whatever time you desire and the camera will fire in burst mode as long as the timer is sending the full button press signal to the camera, just as if you were physically holding down the camera's shutter button.
I've been using the generic model linked above for over four years and it has held up fine.
Another option is to shoot tethered to a computer via EOS Utility.
There is a way to fire off 3 exposures in self timer but it is a bit of a "work around'.
If you use Auto Exposure Bracketing along with the Self Timer, the camera will fire off 3 exposures in quick succession. Using 1/3 stop bracketing won't vary the exposure by much.
I think the answer I put into the link below may help with this question as well.
I am unsure about EOS Utilities working for the number of shots in a row but an Android App Called DSLR Controller (Beta) works really well with my T4i and when i had a T2i. I havent tested it for the 7D mark ii yet. If you can get a micro usb to micro usb or an android tablet with a USB Port for the standard cord. the app lets you program lots of settings like number of pictures, at how many seconds apart, aperture, shutter speed, iso, change settings by brightness after each photo, etc.
I used it for a time laps of completing the patio in my backyard a few years back and it worked pretty well, to make a time laps of my buddies wedding head table, to get self photos where 10 seconds isn't enough time to get behind the camera, review my RAW images while I'm on the road some where and want to see it on a larger screen.
I would really recommend looking into it and see if it might work for your Canon Camera.
DSLR Controller (BETA) - it costs about $7.99 (CAD or USD, i forget)
Remote Release - A Test app before purchasing the DSLR Controller