To the best of my knowledge, they have to be linear.
So, you have to do two things:
1a) Either change S3 to a 4way and get it in chain with the other 4ways.
One way to do that is to use the travelers from S2 to connect S1 to S3 and
run a new cable from S3 to whatever S1 was connected to, or
1b) Leave S3 a 3way, change one of the 3ways to a 4way and run a cable from
it to S3. You might have to run 14/3 to have enough wires if you do that.
2) Somehow get the light on the same hot as the other lights. There should
be some way to do that using either the neutral from S2-S3, or a wire in the
Without any knowledge of how either circuit is wired, or the design of your
house, it is tough to be more specific. Just remember that the hot for the
S2-S3 circuit is now surplus and can possibly be used for something else.
Good luck. One thing to remember if you have metal boxes, the current
through any hole must sum to zero; some rewired circuits like this don't,
and it is potentially dangerous.