At the moment, the Critical Hit description about multi-hit moves is a bit ambigous:
Critical Hits:
A critical hit adds three (3) BAP to any attack before applying weakness  and resistance. Critical hits ignore Reflect and Light Screen, ignore  the Base Attack Power drop from the Burn status, and only apply stat  boosts if positive boosts exceed negative boosts. Super Luck increases  the 
Critical Hit Stage  of a Pokemon by 1, and Sniper increases the damage dealt by critical  hits to five (5) instead of three (3) for a one-hit move, three (3)  instead of two (2) for a two-hit move, and two (2) instead of one (1)  for a multi-hit move.
The main culprit, as many of you know, is: if one of the hits of a  multi-hit moves crit, does the entire damage goes past  screens/burn/stat changes? At the moment, if we go for the most strict  interpretation of the text, it does, and it makes multi-hit moves  incredibly disruptive. While this may add a layer to strategies and  such, I find the disruptive potential a bit excessive. Even in-game, the  best option to use against a foe behind Reflect and with multiple  Defense boost could be your multi-hit move if you have a good one, but  the effect is nowhere as gamebreaking as in ASB, where the difference in  dmg may be incredibly steep.
Now, the discussion wouldn't be complete if I didn't propose a solution to the issue, so there it is. 
My  proposal is that, if a multi-hit move crits, one or more times, against  a foe under the aforementioned conditions (burn, screens, stat  changes), the move gets a damage boost called Pierce. Each crit  grants a Pierce bonus damage equal to the Crit bonus + 1 (So, it would  be 3 for a move like Double Kick, and 2 for a move like Pin Missile). If  the Pierce damage would raise the dmg of the move at or above the level  it would reach if it ignored screens/burn/stat changes, you just  calculate it in the old way. Since it may seem rather strange of a mechanic, and since my wording is obviously horrible, let me give you an example:
Ex1: A Hardy Syclant with no items and Technician uses Icicle  Spear against a Hardy Mew behind Reflect and with +1 Defense. Icicle  Spear hits 5 times, and crits twice. Let's try to calculate the dmg with  my newly proposed system:
4*5*0.67 [Base Power] + 3 [STAB] + 2 [Crit] + 4 [Pierce] - 1.75 [Stage Dif] = 20.65 damage
And now with the old system
4*5 [Base Power] + 3 [STAB] + 2 [Crit] = 25 damage
Since the "Pierce version" does less damage, you would apply it over the "old version"
Ex2: A Lonely Syclant with no items and Technician uses Icicle  Spear against a Lonely Mew with +2 Defense. Icicle Spear hits 5 times,  and crits 3 times. Let's try to calculate the dmg with my newly proposed  system:
4*5 [Base Power] + 3 [STAB] + 3 [Stat Dif] + 3 [Crit] + 6 [Pierce] - 3.5 [Stage Dif] = 31.5 damage
And now with the old system:
4*5 [Base Power] + 3 [STAB] + 3 [Stat Dif] + 3 [Crit] = 29 damage
Since the "old version" does less damage, you would apply it over the "Pierce version"
Ex3: A Hardy Hitmonlee with no items and with Burn status uses  Double Kick against a Hardy Snorlax behind Reflect. Double Kick crits 1  out of 2 times. Let's try to calculate the dmg with my newly proposed  system:
(3*2*0.67 [Base Power] + 3 [STAB] + 3 [Stat Dif] - 3 [Burn] + 2 [Crit] + 3 [Pierce]) * 1.5 = 18.03 damage
And now with the old system:
(3*2 [Base Power] + 3 [STAB] + 3 [Stat Dif] + 2 [Crit]) * 1.5 = 21 damage
Since the "Pierce version" does less damage, you would apply it over the "old version".
While apparently convoluted, my proposal has the advantage of giving a  partial boost to crits of multi-hit moves under burn/screen/stat change  conditions, without making it gamebreaking - in the same vein with how  it works in practice in-game. Thanks for your attention.
P.S.: If you can reword it in a nicer way, props for it.
EDIT: I'd like to add that, unlike what it seems, most times you wouldn't have to do two calculations every time. The above ones are just for the sake of the example. If a multi-hit move crits only once (which is the most common scenario), or even twice for a 4-5-hit move, you will always apply the "Pierce method", no need to doublecheck.