We are remodeling our basement and adding can lights. There are currently 3 drop cord lights in the middle of the areas we are adding the can lights. Can I wire the can lights to each other then to the drop cord light since it is already tied into the breaker panel then wire to a switch? I am adding a diagram. Thank you.

You should change out to greenfield, smurf, or romex, if allowed, The drop cords may have been for single fixture. I take it the 3 drops are switched separately? Are these on own circuits?

I'm not sure I understand the question.

You are removing the plug in lights right? Or are they not plug in?

I would remove the existing lights and just wire the recessed lights as normal. Use the existing feed if it does not have much on it, such as only the basement lights.
You are adding a ton of recessed lights so a circuit for them would make sense.

Thank you Stratmando & Stanfortyman. We are changing to Romex. The 3 drops are switched separately but are on the same circuit. We are removing the existing lights but if wire the cans to the existing feed (except for in the bathroom), will that work? There are 18 cans. What about the outlets? Would it be better to put 9 cans with the outlets for one side of the basement on one circuit and then the other 9 with outlets on a separate circuit? Thanks!

I would not wire nine cans with ANY receptacles. Not that I don't mix lighting and receptacles but nine cans is a lot to mix with general use receptacles.

If the cans are 75 watt max you can have them all on one circuit. If they can hold more I'd split them up to two circuits for just the lights.