I have a 3 way switch, then a 4 way switch, then a 3 way switch. Can I wire the lights on the travelers between the first 3 way switch to the 4 way switch? The power from the panel goes to the 1st 3 way switch.

Not sure I understand you question.

Power goes to first 3-way, then through travelers to 4-way, then to through travelers to second 3-way switch. Power goes from second 3-way switch to light fixture.

You cannot put the light fixture between the switches. The light fixture can be physically between the switches but not electrically.

Today, I have the following wiring setup. Power---> lights---> 3-way switch---> 3-way switch.
I want to know if I can do the following (not likely, but can't hurt to ask).

Power --> new 3 way switch ---> put lights on one traveler --> replace 3-way switch with 4-way switch --> 3-way switch.

Based on your reply, I can't do this. I must run the lights from the last 3 way switch. Correct?

That is correct. Power must go through all the switches. From your second post it appear that what you really want to do is add a 4-way switch with the power coming to the light fixture. That you can do.

I do believe that only the ends work. I never liked those diagrams. A 3-way switch is basically an SPDT switch, so the poles are the travelers.

The 4-way switch is basically a DPDT switch wired with the end positions crossed. It's wired like a fan reversing switch or a DC polarity reversing switch.

There may be some expensive wireless options that can minimize wiring.

KISS

I don't think I understand what you are saying.

OP has power being fed to fixture and two 3-way switches. I am betting that the travelers pass through the light fixture box. If he can get two 3-wire cables to the desired switch location and there is enough room in the box for the additional wires, another switch (4-way) can be added.

I need to draw a diagram and I'm bad at doing them.

ASCII ART

... [a]****%1*****[a1]
[b]... [b1]
... [c]*****%2****[c1]

In a typical 3-way switch arrangement [b] is switched to [a] or [c], a typical SPDT switch and the effective switch is between [b] and [b1]. The "*"'s are wires.

What a 4-way switch does is to cross points %1 and %2 and they can be crossed n-times.

I understand how the switch works.

Quote:

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I do believe that only the ends work.

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I don't understand that statement unless it means ,

"No you can't tie into the middle of the switching system. The switching system being the entire series of switches. Current must enter the first switch and be taken from the last."