Need Help Adding Another Switch to Lighting Circuit
You need 3 conductors (+ ground) between the old switch and your new switch. That's your biggest issue. Once you have that, there's inevitably a way to wire up two new 3-way switches to work.

If you are thinking about using 2 existing switches, there's a very low probability that you have the necessary third wire ("the traveller") available. (In the question you linked, the traveller is drawn in red.)

((edit to say that this answer is useless... I'll delete after the dust settles because the OPs comment is relevant.))