Timing constraints, collection naming, tool flow, and clock gating

You can't have a clock in more than one -group within a single set_clock_groups assignment. (Not sure why, as it would be nice). Using multiple assignments, there are multiple ways to do it. I didn't follow exactly what you want so don't take these as literal solutions, but:

1) You could cut clk3 from everyone else first:

set_clock_groups -asynchronous -group {clk3} {clk0 clk1* clk2*}

Note that I also used wildcards, which can help with readability, but has it's own dangers...

Then do individual groups, like:

set_clock_groups -asynchronous -group {clk1a} -group {clk1b}

set_clock_groups -asynchronous -group {clk2a} -group {clk2b}

This cuts timing between the multiple clocks coming out of a single mux, but leaves everything else related(the default), so clk0 is related to everything, clk1a is related to clk0 and clk2*, etc.

Is that close?