I usually deal with this by having several instances of Word open. All the alternatives seem worse to me.
When I have to refer to several docs at once and there’s any I need to look at but don’t actually have to copy into or out of (such as a reference doc or review comments), sometimes I use two computers side by side, a laptop alongside a desktop.
If you can eliminate one or two of the files you have to have open, such as by consolidating comments or combining reference data, that will make it much easier. If you want them on tap even though not actively open every second, you can always get to them from the File dropdown list of recent files. I have that set to the max of nine and wish it would allow me twenty.