To the best of my knowledge there is no way to take multiple images with a single press of the button using any of Canon's IR remote shutter releases such as the RC-6. This is because a constant signal from the remote would deplete the battery supplying the energy for the remote very quickly.

On the other hand, almost every wired remote I've ever seen includes the ability to 'lock' the button down. If the camera is set to continuous shooting mode it will take one frame after another until the memory card is full, the sensor overheats, or the battery is exhausted. I would consider getting a wired remote compatible with your 60D, such as this one from Canon or this generic one. Or even one that has a programmable intervalometer. I've used the version of the Neewer with the N3 connector (fits 7D, 5DII, etc) for several years without any issues. I've also used generic versions of the simple one button remotes. Some are built better than others, but the genuine Canon RS60 E3 is only a little over twenty bucks at amazon.

For more on the advantages of a wired vs. wireless remote, see this answer to Can I use a remote shutter / bulb mode on a Canon T4i?

(Re: the Neewer remote. Ignore all the reviews that complain about having to remove the batteries between uses. It is like a digital watch, the batteries last for years unless the timer is set and running to continuously trigger the camera when you store it. If you put a digital watch away with the alarm set to beep constantly the batteries will die quickly also, but if you turn the alarm off the watch will run for years on a single battery. I've replaced the batteries in my Neewer remote once since I bought it over two years ago, and that was fairly recently.)