Well "it depends"
The first issue is whether the power supply is suitable - both sets would need to be the same voltage and type (either both AC or both DC), and the power supply would need to be rated to run both.
The next issue is that if you look at most low voltage sets these days one side of the supply does not go to the end. Typically there's a number of LEDs in series to make a small set, then multiple sets are wired in parallel. You'll see this as 2 wires going as far as the first light, then 3 wires for the next few lights, then back to 2 wires for one gap, and so on. Some sets have 3 wires from the controller box to the first light, then as many as 5 wires within the string.
So you need to tap into the right wire at the end LED, and run an extra core back to where you can pick up the other side. This won't be easy to do neatly.