This is an exploded view of a post top tenon when the post is at the end of the plate. The tenon is 2″ off the side of the post and 2″ thick. The tenon is cut back 2″ from the face of the post so that some “relish” is left on the end of the plate mortise. The post is reduced down to the next one-half inch in the side as part of the standard process to size the post at the joint.
Any reason why you wouldn’t cross pin through the relish with an additional pin to help stabilize the end of the timber in the relish area? Would that not help reduce end checking and further reduce cracking the relish during raising if the bent/aisle racked?
You can add another peg if you would like but in this case, I would not recommend it. As the plate begins to shrink as the timber dries the upper peg could potentially hang up the timber there leaving a gap at the bottom or with the added pressure could break out the relish. If you are worried about raising day, and you should be because I have broken a tenon did it, you can add some additional temporary bracing to shore it up before lifting it up.