I had a friendship/relationship with my already engaged
colleague and now she cheating on me with someone else.
She knows I am aware of this double/triple timing but she
is indomitable and says "I showed her the way". She knows I
like her a lot and often abuses me profusely. Must I get a new job? How do I manage this?
She blames you, saying "You showed me the way". But she must take responsibility for her own actions. That other people have done similar things does not, of course, free her from responsibility.
It sounds as if you still are very fond of her. I wonder if you would accept it if someone else treated you the way she is treating you, or would you be able to put your foot down and declare limits to what
You have a choice. Either continue under her dominance and
accept the way she treats you, continuing to live with the hope
that she will continue giving you favors.
Or you can declare what is acceptable, and distance
yourself from her. Hopefully, this will make her stop
treating you badly; but there is of course a risk that she
will get angry.
You could also ask her nicely to treat you with respect and
suggest that you should have a more grown-up and civilized
relationship in the future.