Haven't actually played multiplayer, and there's no actual documentation as to how things differ from singleplayer to multiplayer so some of these thoughts are kinda at a guess.
Some of the items are also generic things I noticed too, rather then game specific.
Enemies moving as a group: probably want to break out the melee guys at least, otherwise in a mix with tanks and slow stuff they're target practice.
Parasites: TL difference between target and attacker should change chance of parasiting. Target is equal level, 100%. Target is one level higher 50%. Target is two levels higher 25%, three levels higher 12.5%, four levels 6.25%. This should fix the last of the "too powerful" issues, plus make it a little harder to get a force of ships higher then your current level.
Turrets parasited by an enemy whilst building immediately begin attacking, even if they only just started being built by the player (so of course could not attack yet).
There needs to have two different types of "lightning missiles". One type being the current one, fast and good against starships. Another type being somewhat slower, having larger radius, cost less +AI, and do less damage, basically to help taking out things underneath forcefields. In Fast & Dangerous mode at late game on IV/III planets, it's more they're more like playing Slow & Deadly mode (since you have to wait for more ships to be continually rebuilt since it's rare not to loose your entire bomber squadron just to take out a single forcefield), and also Repetitive & Boring since it happens so often, and they take so long.
Just some notes as to the difference between multi/singleplayer from how I would have assumed a few things would have worked:
You start start with base crystal/metal rather then 8x the start amount (start "total" for all players).
Ship caps seem to be normal rather then 8x. Could cause problems late in the game. Or for that matter even early in the game. I've got 8 external wormholes, and only 170 fighters/bombers/cruisers to split between them. (plus assorted random ships) Should only affect Probably Tech I fighters/bombers/cruisers really, and maybe Tech II/III, I don't know how knowledge harvesting is handled whether it's 2000 per player per planet or just 2000 per planet. Shouldn't multiply your special ships though.
Immediate access to eight times the amount of knowledge, at eight times the normal rate gain. Probably should only give the player one science lab and force them to either buy more themselves, or traipse it around the place.
16 advanced factories but only 12 data centers? Might be worth dropping the number of advanced factories down. Want to tell where the AI's HQ is? Follow the trail of every-planet-that-has-an-advanced-factory.
Also it meant it was really easy for me to grab one as well, there was on in a system 2 hops away.
8 planets sucked dry, and I've got 1976 knowledge left over. It looks like that rounding bug is still there.
Some seeds on 80 planet simple for packs of planets with no more then 8 vulnerable wormholes:
208984376
820800782
6: 166992188
7: 75683594
852539063
1936035157
1382324219
8: 1224609376
339355469
1994140626
783203126
834960938
1395507813
387695313
38574219
654296876