Common-mode chokes in series
Yes to caveats. The common mode choke is not magic, being instead one leg of a voltage divider. The common mode chock is the series element of the divider.
You need to provide a shunt element, for the choke to be effective. You can explore several shunting methods

(1) shunt between the +/- pairs only

(2) shunt from each of the differential wires to GND/RETURN

(3) combining 1 &amp; 2