Yes, but why? What problem does that solve for you? It's a complication I try to avoid unless there's a very real need for it.
You could just put a different copy of this field elsewhere and when you select your value from a list there, you'll see the selected value appear in the field where you've currently located it.
There are also ways to set up a script trigger for a script that uses Set Field to copy the value in a field where you've defined this drop down or pop up to your original filed--but again, that's an added complication that is fairly unusual.
You can also use new window to pop up a small window where you have a layout designed for such structured input and there are ways to make this floating window act like a modal dialog where you can't interact with the rest of your database until this small window is dismissed.
Ah, of course. Just added a second copy of the field with a different value list attached.
Attached the 2nd valuelist to the copy, assigned it an object name, placed it behind the first copy. Then added a button which selected the 2nd copy by object name.
So when the top (normal) copy is selected, the 1st value list shows. When I click the button next to the field, the 2nd valuelist shows, all transparent to the user.