Splitting Load b/n 3-way and single pole switch

I am re-wiring some electrical work in my basement and have a questions as to how, if possible, I can split on the incoming power between a 3-way switch and a single pole switch. Here are the details: power comes in via 14/2 wire into a 3-way switch ("Switch 1") which goes to the existing gang box of another 3-way switch ("Switch 2") via 14/3 wire and then onto a light fixture via 14/2 wire. I would like to add a single pole switch next to Switch 2 but use the power coming into the Switch 1 gang box to power the lights I would add to the new single pole switch. Is this possible and, if so, how would I wire the new single pole switch?

Thanks.

 

Not possible with the existing 14/3. You need to run a new 14/2 from the switch 1 box to the new switch.