Here is your quick answer:
No.
Any questions?
What I would do is a "save as" and then add/remove what you don't want. That's how it must be done.
MyDMX doesn't look at the UNIVERSE as one item and then your scenes as an unrelated item or set of data.
I can understand the other point of view. Let's say you work with 5 bands and some corporate jobs. Each uses the same UNIVERSE, or at least you're not changing your addressing for your lights, so everything is at the same DMX location all the time.
Each band has their own light shows, and then the corporate things have their own much simpler shows.
But no, in this case, you can't copy between sets.
If you want to copy your scene within the "show", you can do that, and rename and edit as you see fit.
For example, I have a "white wash" scene, basically, my 64 LED Pros, full on(all RGB channels up and the master dimmer UP all the way). Then, as that as my starting point, I then copied it a bunch of times, and then changed the colors(pink, red, yellow, amber, blue, green.... you get the idea) and named it to match.
Similarly, did a scene with my moving yoke lights drawing circles on the wall. I copied this scene and on each new copy, I used a different color on the color wheel.
Making sense?