Extending \IPS\Member with new bit options?

I am extending \IPS\Member and I need to define more bit options. How do I do this?

Specifically, I assume I need to extend $bitOptions to add the new bit option values. How do I do this? 

My new bit options will be stored in a new column (not members_bitoptions or members_bitoptions2). My app requires 5 profile completion steps so I need to store the completed steps in bitoptions to keep from having to create separate columns for each completed step. My app also requires around 7 other bit options to be tracked for each logged in member.