Can I install Mavericks side by side with an existing installation? My current installation of Mavericks has some issues that can only be fixed with a clean install (no Time Machine restore).

However I don't find time to do the complete reinstall in one session and I still have to work with the current installation.

Now my idea was to install the OS just parallel to the existing Mavericks once more. I have already shrunk my partition (see image). But I fear the second installation will kill my current one if I now just reboot and select to install Mavericks.

Any comments/solutions?
Yes, you can install OSX onto any eligible partition or external drive and are not constrained to simply apply it on the running OS. 

Download the installer and choose any destination when it prompts you to install over the running OS. 

I prefer this in almost all instances since I can run the migration to my new OS without ever losing my current setup or wiping a system that is currently in use. It only costs disk space and one extra step when installing.