I watched the movie last week, not for the first time albeit, but not one of the pushers in the movie ever pushed themselves.
The pushers could push any of the other 'unique' power groups...and believe me there are a lot.
Stitchers - could heal just about anything with their touch, not painless though, the polar opposite.
Watchers - Dakota Fanning was a watcher, but she was young, inexperienced. She could see glimpses of the future in pictures, she drew what she saw, she was a shitty drawer...her mother though, stated to be at the top of every 'watch' list the Division had, and I mean the most dangerous as she could see clearly, and easily into the future the most that was stated was 13 years...as she already new the events of the movie before she was captured and before Dakota's character was born, who was 13.
Shadows - could conceal people from watchers vision, it depends on the person; how well they can be shadowed, how long and how effective they are, the power gauge can go from just small objects to people to entire buildings(RARE)
There's plenty others, google it.
But from what the movie shows...a pusher never pushed themselves, and was never stated to, but a pusher can push each other.
Also, the main antagonist of the movie was a pusher, the agent who shot his partner in the back of the head, was then pushed into shooting himself in the head(mouth). The antagonist told him to take time off and go on vacation, the agent insisted he was fine and he won't be pushed again, the pusher then said are you willing to risk your life on it, the agent who was a sniffer(I'll get to that) just looked shocked and scared, the pusher looked him In the eyes and had an inner monologue moment, he said out your gun inside your mouth and pull the trigger. the agent was hesitant but pulled the gun out ready to blow himself away, the pusher then said, don't worry you emptied the bullets out before..a flashback of the non-existent events came to be, and he...well...blew himself away.
It was effortless for the pusher.
A sniffer can track any objects movements, travels, actions etc by simply touching and sniffing an object.