Yes, It is possible to have Unity and GNOME installed at same time. Here's what I did: I installed Ubuntu GNOME 13.04. Then I installed GNOME 3.8 via PPA. Later(After using GNOME 3.8 for months) I installed Unity on my machine.
For instructions to install latest GNOME on Ubuntu 13.04, go to : Is it stable to install GNOME 3.8 on Ubuntu 13.04?
To install Unity I used :
sudo apt-get install ubuntu-desktop
In your case, You may install latest version of GNOME using link above. During installation it will ask you for default DM (Light-DM or GDM). Choose either. Reboot and choose your session from Login Screen (Ubuntu or GNOME).
When you run GNOME, if your desktop still looks like Unity, then you may need to change current theme, cursor theme, icon theme, gtk+ theme etc. using "gnome-tweak-tool" (To install :
sudo apt-get install gnome-tweak-tool).
If you don't want to use GNOME and want to use Unity, just logout and choose your session from Login Screen (Ubuntu or GNOME). After running Unity, you may need to change current theme, cursor theme, icon theme, gtk+ theme etc. using "gnome-tweak-tool" (I needed to).
If you want to change default Display Manager, this may help: How can I make LightDM the default display manager?