python scrip that moves files in multiple threads.

I have a python script that I made that searches for files from a list of directories and then copies them to a list of destinations. Right now I am using with Pool(processes=threads) as pool: to move 4 files at once. The problem is that if one of those files takes two times longer to move then it holds up the whole queue because it can't move 4 more files until ALL of the first 4 files are done being moved. I would like to update this script so that it can move up to 4 files at the same time and if any of those slots finish it can be filled in with the next file to move instead of having to wait for each group of 4 files to finish completely. This should be a pretty simple job for someone with python experience. I am including the script to update here.