With the exception of the monument, there is not much to see at the top of the mesa. If you trek a couple of hundred yards west of the monument, you will come to an old barbed wire fence that marks the border between Oklahoma and New Mexico. But you will be able to say "We were there!".
After completing the Black Mesa trek, we drove north from the parking lot to the Colorado border (only a few miles). A left turn onto a gravel road at the border and another mile or so will bring you to the marker where Oklahoma, Colorado, and New Mexico meet. You can be in three states at once. Not quite four corners but close.