Can you mix water colours with acrylic paint?

No they are still oil paints, they have been made water soluble but are still not compatible with other water based media.
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You can use water mixable paints (WMO's) over acrylics very dramatically. You can do the background and what ever else you want with the acrylics, let them dry completely, and wipe on a very fine layer of WMO linseed oil or my preference, walnut oil from M.Graham.
Wipe off any excess oil. You want this to be very thin so it acts as a binder to the acrylics and makes them go on very smoothly.

You are free to paint large areas of just small high lights with the WMO's. What ever you want. The paints will dry slower than the acrylics, but wash up with soap and water just like acrylics.

For more discussion on WMO's and Walnut oil, go to the link below, WMO;s
Judy Filarecki