Mark records that Jesus goes on to say:
43But it shall not be so among you. But whoever would be great among you must be your servant, 44and whoever would be first among you must be slave of all. ESV
So you could ask "who in the Bible most fits that description?". An argument could be made for Paul or perhaps one of the other apostles, but I do not think Jesus has in mind a literal pair of people when he speaks of his left hand and his right hand, even if James and John do. This would be missing the point I feel.
Rather Jesus intends to subvert the whole idea of greatness in the mind of James and John:
42And Jesus called them to him and said to them, “You know that those who are considered rulers of the Gentiles lord it over them, and their great ones exercise authority over them. 43But it shall not be so among you. But whoever would be great among you must be your servant, 44and whoever would be first among you must be slave of all. ESV
They think that the position of highest honour is at Jesus hand as he sits on his throne, but rather it is by his side in his suffering and death:
45For even the Son of Man came not to be served but to serve, and to give his life as a ransom for many.” ESV
As the hierarchy of greatness is turned on it's head, so is the need for this position on honour to be strictly limited to a small number of people: the worldly idea of greatness is by it's nature a pyramid with fewer and fewer people as you climb higher and higher. The concept of greatness Jesus introduces them to has no such inherent restriction. James and John (and you and I) can be great, he says. The problem is not that they are not able, it is that they have no idea what true greatness is:
38Jesus said to them, “You do not know what you are asking. Are you able to drink the cup that I drink, or to be baptized with the baptism with which I am baptized?” 39And they said to him, “We are able.” And Jesus said to them, “The cup that I drink you will drink, and with the baptism with which I am baptized, you will be baptized, ESV
In a figurative sense, those who have the position of highest honour are those who are crucified at Jesus left and right hand. Not the two criminals literally, but those who take up their cross and follow Jesus.