How does Lightning Arrow interact with Multiple Projectiles?

Currently for me each cast of Lightning Arrow will chain it's damage to a maximum of 4 nearby mobs. My question is, when augmented with Lesser Multiple Projectiles, which adds 3 total lightning arrows, will each of the three original arrows spread its chain damage to a potential 4 nearby mobs?

In other words, if I use Lightning Arrow with Lesser Multiple Projectiles, and I have 3 enemy mobs in front of me, if I hit each of them with an arrow from a volley, will each of them receive 3x damage? That is, 1x from the original damage, and then twice as chain damage from the other two mobs adjacent to them.

Also I presume that each of the three arrows preserves its ~40% ability to shock?

Thanks for answering :)

Yea, I am pretty sure that's the case, it is with Poison Arrow and it's the same idea, original 1 arrow gives AOE damage as well as initial impact damage. Also keep in mind that multiple projectiles gem takes some of the damage away, so while you do get triple the hit each of the arrows would hit for less damage. I am not sure about the chain damage, however, without damage numbers in the game you can only guesstimate that, but I think for balance reasons the chain damage stays the same, what you get is having a bigger chain due to more projectiles so with a larger group of mobs more of them will get hit with chain damage. So for 3 mobs the damage with multiple projectiles will be larger, but you get main benefit from hitting, say, 12 mobs where all 12 of them will receive chain damage due to 3 arrows hitting (assuming they do).

Indeed, if this is in fact true, then the max total damage including splash would be 0.7 * (1 to 5) depending on how many mobs were in the group.

Of course, you have to add in the chance to shock, when comparing it to other DPS. Right now I'm comparing Lightning Arrow with Multiple Projectiles to Frenzy with Multiple Projectiles. It's hard to eyeball test how effective Lightning Arrow is because of the highly random nature of lightning damage. But it does currently seem like the Lightning Arrow is superior to Frenzy for AoE damage. The only issue is that I need to take extra care to keep my Frenzy charges up.

The good thing about Lightning Arrow is that it "automatically" aims to nearby enemies, as we know, it can be hard to get multiple projectiles to correctly hit 3 enemies, and this may put Lightning Arrow ahead, despite Frenzy having an insane attack speed.

If anybody knows the answer to this for sure, please post!

Yes, it works like that. You can also get a similar effect with piercing. The lightning will occur for each enemy an arrow hits.

A related question: If I add chain support (or get the ascendnacy passive skill as deadeye), then can it chain with a target that has already been hit by another projectile / bolt or does it only mean that instead of hitting 4 nearby mobs I hit 5?

Pierce overrides chain.