In Leviticus 16:15, after atoning for the priesthood inside the Most Holy Place using bull blood, Aaron is instructed to exit the sanctuary, sacrifice the Lord's goat, and enter the Most Holy Place again, atoning again using goat's blood this time (for the people). After this, he performs further atonement for the Tent of Meeting and the altar of sacrifice. Based on Leviticus 16:18, it appears that this is done with both blood types at the same time. Why did the high priest need to finish the bull offering's MHP atonement before performing Israel's MHP sacrifice and atonement? Couldn't he have killed the bull and the goat at the same time and brought their blood in at the same time? If the rites were meant to be separate, it makes more sense to me that he would wait until all three compartments are atoned for (MHP, tent, altar) with bull blood before beginning with goat blood.
Also, if it helps anybody process it, it appears that the sacrificial goat and live goat were determined in between the Most Holy Place atonements. 16:6, which is cited in 16:11, is followed with the selection of the two goats. Hence, the goats are selected in after the bull offering's atonement, in between the two MHP atonements.
