What is the word for trying to do someone else's job, to get them fired eventually?

I have been searching a lot for this, but can't find the expression. I'm wondering if there is a phrase that is used a lot for this.

At work, it happens a lot in many organizations that people try to do someone else's job to show off themselves and their capabilities. The motivation behind this is usually either to get a raise, or to show their boss that the current person is not doing their job well enough, and they can replace that person.

Is there a phrase or expression for this act?

The closest I can think of is being after someone's job. This is a common and idiomatic expression.

However, being after smb's job can manifest itself in many ways. It's not limited to doing someone else's work. It can involve scheming, currying favor with superiors, etc.

The guy's great with manipulating superiors but I can see right through him. ... He hasn't got what it takes to do his job: no creativeness or any idea of quality. ... Now he's after my job 'cause I'm the only female there with any power and he dislikes me clearly.

(typologycentral.com)

May I suggest "to sideline".

to Sideline is defined as :

to prevent (a person) from pursuing a particular activity, operation, career, etc

You can use it like this :

John pushed Josh to the sidelines on the new project as a first step in his campaign to replace him

Consider, tread on someone's toes/turf

also, step on someone's toes: to offend (a person); encroach on the territory or sphere of responsibility of (another). Random House