How to use W3TC with Domain Mapping seems to be a common question on these forums. I've done some QUICK testing and it appears with the following Super Admin > Domain Mapping settings W3TC will work fine.
IP/CNAME with standard settings
Remote login - disabled
Permanent redirect - either option
User domain mapping page - either option
Redirect admin pages to original domain - disabled
With these settings the same URL is reported on both the front-end and in wp-admin which is where the issues with W3TC occur.
The trade off is that you need to log in to separately to each mapped site but, in my view, that's a minor issue and what you'd need to do if you were running separate WP installs.