I did my "Go big or go home" with the TEC on "Systems of War" (4 players, 5 systems), and did a 2x2 with pirates enabled. So I did have frigates - my ally's, and the pirates

. Normal difficulty only... I regard special restrictions to be an inherent "hard" setting, and see no need to bump it up further.
Key to this is to realize that capships are SLOW. Therefore you have to figure out where you need to be well in advance of being there. If you get attacked in a system and you don't have a cap nearby, give up on that system, build fortifications on the nearby ones, and task a force with an Akkan to throw back the assault and retake the worlds.
The capship slowness also means, paradoxically, that you have to outexpand the AI at first in order to be competitive later. You need to begin with 2 Akkans and take as many worlds as possible before the AI catches up. I had begun on the central system before the AI finished their home systems (note that on hard, the AI will outexpand and eventually kill you). Your need for cash and hence trade is critical: you must purchase capship upgrades and ensure your enemies are too preoccupied with pirate raids to hinder your desperate expansion. That also means that contra the first commenter's advice, you MUST upgrade homeworld immediately like normal. Otherwise you get the second cap earlier but you can't pay for upgrades.
Then I built the following order of capships:
Kol, Dunov, Kol, Kol, Dunov, Kol, Dunov, Sova, Mazra, the rest Kol's.
I probably shouldn't have built 3 Dunov's - You fight on 2 fronts often, 3 not so much. Once you get a Dunov/Sova/Mazra combo, its time to harass the enemy with it. Eventually add an Akkan and maybe a Kol and the will mop up worlds. 2 Kols and one Dunov can handle medium-size threats, and 1-2 Kols should play defender at each of your star systems.
Capships are not enough firepower to fight off the enemy: You also need fixed defenses. Fortuately, you are playing against normal AI, so they can be relied on to mostly attack the nearest planets. At each heavily contested world, you eventually want four hangers, 1 pji, 2 repair bays healing each other, and one turret to fight off close-range attacks. This will hold the world until the patrolling capship(s) can help. This combo, if all-bombers, can survive a max-pirate assault with only nominal capship help.
Key abilities:
* Shield restore: any time you face a major attack, this Dunov ability will keep the Kol(s) going forever.
* Targetting uplink: Because you need every shot to count, and what else are you going to spend the point on?
* Flux field: Turn this on then set all Kol's to spam railgun shots and flak while recharging with...
* Finest hour. The only way you are going to get the firepower you need to kill enemy fleets. Remember to get the Kol right in the middle of the enemy formation to use all guns.
* Embargo - no reinforcements for you! Give me some money for upgrades!
* Radiation bomb, EMP charge: Any attack that affects multiple ships is something you NEED. Now. Because you will always be outnumbered, and every shot that isn't killing hull is a wasted shot.
* Armistice: Suspends the battle until the Kol(s) arrive or if you need just a little more time to install those tatical buildings.