If you want to install Apache Openoffice alongside Libreoffice on Linux Mint 16 or Ubuntu 13.10 Saucy Salamander, you may try this way.

First, download the Apache Openoffice from the official website and extract it any where.
Install the deb file in DEBS directory except deb file in desktop-integration directory (we will install it later) with this command (don't forget to entering the DEBS directory in terminal) :

sudo dpkg -i *.deb

Ok, if you done install the deb file from DEBS directory the next step is install deb file from desktop-integration directory with this command :

sudo dpkg -i --force-overwrite *.deb

That it's, you can find the openoffice on the office menu.

Note :

if you have problem with libreoffice-calc (assigning formula crashing the apps), just delete the libreoffice directory in "~/.config/libreoffice".