Can one do both zazen and centering prayer(contemplative prayer) at the same time?

I meditated regularly for years doing zazen, in the tradition of korean and japanese zen. i then discovered within the christian tradition a form of prayer that's theologically sound and rooted, and it seems similar to me with zazen in that the prayer/meditator is not trying to do anything. i reckon centering prayer is different, because the intent is still opening yourself to God, whereas in zazen there is no intention of opening to a higher power, but at least in shikan taza (just sitting), it seems zazen itself is enlightenment. you sit for the sake of sitting.