[kbsparky]

I'd opt for a sub-panel to replace the dryer outlet. Then one could run 120 Volt circuits for the standard receptacles, and a separate 240 Volt circuit for the radial arm saw. Separate breakers for each circuit.

 

[mpoulton]

here it is straight from the nec

210.4(C)
Line-to-Neutral Loads. Multiwire branch circuits
shall supply only line-to-neutral loads.

Exception No. 1: A multiwire branch circuit that supplies
only one utilization equipment.

Exception No. 2: Where all ungrounded conductors of the
multiwire branch circuit are opened simultaneously by the
branch-circuit overcurrent device.

I don't see any ambiguity whatsoever. A MWBC with a double-pole breaker is clearly permitted to supply both 240 and 120V loads. That's the entire point of Exception 2.