Can I bind my mouse buttons in-game?

I just got a Razer Naga 2014 and it has 12 side buttons. By default they are assigned to the 1 through = keys at the top of the keyboard. But instead of binding them to physical keys and then binding those keys to in-game actions, is it possible to just bind the buttons directly in-game? What I mean is, go into the Keybindings screen, select an action (such as Hotbar 1, space 1) and just click one of the mouse buttons to assign that hotbar space to that button.

I was able to do this with a previous mouse by setting the button action (in the mouse software) to "Generic," and then I was able to bind those side buttons (only two, Mouse 4 and Mouse 5) directly in the game, rather than bind them first to numbers or letters and THEN bind those numbers or letters to in-game actions.

Is this possible or does the game not recognize anything beyond Mouse 4 and 5?

Thanks.

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- Furlamseere