Timespinner supports a 2-player asymmetric local co-op mode with drop-in/drop-out.
Activating the co-op
Once you get your first Familiars, a secondary player can assume its control by pressing start on another joystick.
The familiar can't get hit, and can move freely around the screen. It can perform a melee attack, and when charged, a special attack, unique per Familiar.
It's also possible to quick-switch familiars by using LB/RB.
Currently, it's required to have 2 connected joysticks to play local co-op, as both the first joystick and keyboard are reserved to the main character/player 1.
Even though the co-op is only local, it's possible to play it online using Parsec, NVIDIA GameStream, or any other technology that allows remote play.