'Behalf' in the Bible

I thank my God always on your behalf, for the grace of God which is given you by Jesus Christ;

Has Christ been divided [into different parts]? Was Paul crucified for you? Or were you baptized into the name of Paul? [Certainly not!]

Now these things, brethren, I have figuratively applied to myself and Apollos for your sakes, so that in us you may learn not to exceed what is written, so that no one of you will become arrogant in behalf of one against the other.

In addition, we are found to be false witnesses about God because we testified on God's behalf that he raised the Messiah whom he did not raise if in fact it is true that the dead are not raised.

Otherwise, what will those do who are being baptized for the dead? If the dead are not raised at all, why are people even baptized for them?