The new backstab progression is inspired from Advanced D&D 1e and OD&D Supplement I, so I'll use those two as the basis of a formal, legalistic answer. On page 27 of the AD&D Player's Handbook, back stabbing is described as follows:
"Back stabbing is the striking of a blow from behind, be it with club, dagger, or sword. The damage done per hit is twice normal for the weapon used per four experience levels of the thief, i.e. double damage at levels 1-4, triple at 5-8, quadruple at levels 9-12, and quintuple at levels 13-16. Note that striking by surprising from behind also increases the hit probability by 20% (+4 on the thief's "to hit" die roll)."
Whereas in Supplement I:
"By striking silently from behind the thief gains two advantages: First, he increases the chance to hit by 20% (+4 on his die). Secondly, he does double damage when he so attacks, with like additional damage for every four levels he has attained. Thus, if a thief of the 4th level attacked from behind he would do twice the damage indicated by the die, at 5th through 8th levels he would do thrice the damage, at 9th through 12th levels he would do four times the damage and so on."
My understanding then is that you would multiply only "the damage indicated by the die", and then apply modifiers afterward, legalistically.
However, I have encountered GMs both old and young who run it as "calculate damage as you would normally, then multiply", and even GMs who include magical modifiers.
Ultimately, due to how risky the backstab maneuver is and how rare it is that players will opt to take the risk, I personally prefer to rule it in that method - with all modifiers applied first, then multiplication, for the greatest possible damage.
I don't think this is supported by the rules-as-written.
But this is the OSR! We do things as we like, and I encourage you to experiment and adjust to the taste of your own players :3