So I asked a similar question several weeks ago & tried a couple of the ideas put forth, but I could not get all the lights to work properly. Here's the full story including some additional detail which may or may not matter.
I installed a new light fixture with the intention of not only connecting it to existing lights, but also combining 3 lights spread over 2 light switches into 1 single light switch.
When I removed the 2 light switches, I noticed they were not wired up with 2 separate lines, instead with a single 4-wire line. So I removed the red wire from both ends & connected the remaining wires, & the lights now light up all at once when turning on the switch.
So then I 1st tried simply connecting the new light to the same light switch as the old lights - in other words 2 black wires on 1 screw, & 2 white wires on the other screw. But the result was that only the old lights worked when turning the switch on, & when turning the switch off the old lights turned off but the new light turned on.
I then asked a question here:
1 of the answers suggested following this diagram:
When I did that, the switch turned on only the new light - the other lights remained off.
When I removed the new light & reconnected the old lights, the old lights worked fine again.
I tried a few similar variations but no luck - exact same result. Tried different light switches too, but same results.
I also tried with a double pole switch - but the new light doesn't work at all - only the old lights worked.
Why does this happen? What can I do to get it to work? A couple of pictures showing what I had tried. The wire going to the top right is connected to the new light. The thick black wire leads to the old lights.