Can I run a 10 speed cassette on an 11 speed wheel, but also keep running 10 speed on a 10 speed wheel?
Use spacers on the 11 speed wheel to put a 10 speed cassette on. 

See your hub manufacturer's page for details, but its normally a 1.8(5) mm spacer (which comes with the hub, but you can buy separately) and a 1mm spacer (sometimes; which you'll get with the cassette). See this page for a table of some common cases.