It is possible to install both versions but it will be counter productive sync your user defined settings from one to other.
Before you proceed further backup your settings. I am going to describe instructions for uninstalling Pycharm Community edition. You can also use this to remove Pycharm Professional edition.
Suppose you have pycharm Community installed at
Use command this command
rm -r ~/ide/pycharm-2016.3.2 to remove it.
You should also remove by these entries by using command
rm -r. This contains your configs/license files for Pycharm.
rm -r ~/.PyCharm2016.3
rm -r ~/.java/.userPrefs/jetbrains/pycharm
sudo updatedb && locate pycharm to check whether other pycharm files are still left. If you any files that has
pycharm in the name which is useful to you than don't delete them.
rm -r doesn't work use
sudo rm -r.