I bought Kim dinner to make him up for being late.
Is "him" in the above optional or must I delete it? Thanks.
I take your point.
But in our mother tongue, we have a similar expression and we usually put in the person to whom we want to make up for something. So I wonder if the following sound right to you?
I want to make up for being late to Jim.
I'd like to make up to you for misunderstanding you.
I'd like to make it up to you for misunderstanding you.
Fine, all those cases with 'to <object>' are fine. Your original sentence had 'made him up'*; so when I said 'one object' I was wrong; you can use two objects, but both are indirect - one for and one to.
*The most obvious interpretation of 'made him up' is 'applied make-up [cosmetics] to him'.