Fabricate as many claims as you can and ALWAYS turn them into a vassal (can be any type). These combined lets you expand for 25% of the aggressive expansion and warscore.

You can easily provoke your vassals into rebelling by using Harsh Tributes button in the economy screen (works on every type of subject). This will let you take all their land for free. The only downside being you have to fight them twice.

VERY IMPORTANT NOTE - subjects of your Culture Group will never rebel against you

When conquering it's important to note the following things:
War Target means the country you declared war on.

Annexing Land
Base Costs
+1 base
+5 if a port
+1 for every 5 pops (if city)
+1 for every 2 buildings (if city)
Modifiers
+10% has pops of your culture
+10% has pops of your religion
+33% not war target (aka the allies or subjects of the country you declared war on)
+300% show superiority wargoal
up to +2500% depending on how small a country is
-10% bellicose diplomatic stance
-25% take province wargoal (can only get this if you're the attacker)
-33% claim on territory
-25% for each rank difference lower than war target (lowest is local power)
This means if you're a local power or city state fighting a great power, you get a -75% discount on all of the great powers provinces
-95% rebelling province

Base Costs
+1 base
Modifiers
+33% not war target
-0.5% for 1 tyranny each
-50% claim on territory
-100% rebelling province

Vassalising countries
Turning someone into a vassal takes all the costs above and HALVES them. So instead of needing 100 warscore and taking 100 aggressive expansion, you only need 50 warscore and take 50 aggressive expansion.

VERY IMPORTANT NOTE - subjects of your Culture Group will never rebel against you

Expanding through vassalising is a LOT cheaper than direct annexation. Combining claims with vassalisation lets us conquer at 25% the cost. Using this strategy as Macedon, you can turn Egypt into a tributary who will never rebel.

Allies of the war target are 33% more expensive to conquer. It's best to fight the biggest nation head on, rather than declaring on smaller allies.

Attacking nations of a higher rank than you are also much cheaper in warscore. If you're about to go to war with a higher rank enemy, it may be worth reducing your rank by giving land to a subject or client state.

Aggressive Expansion doesn't care how valuable a province is. Taking a 1 pop desert territory costs the same as taking Rome or Carthage. It's more efficient to expand into high value provinces rather than empty land. However civilised lands tend to have much lower happiness than tribesmen.

Once you've acquired enough subjects, it comes time to trick them into rebelling so you can annex their lands for free. You can do this by setting Subject Tributes to Harsh in the economy screen.

A subject must be lower than 33 loyalty to rebel. If they're still above that, send them an insult.

You can check a list of your potential rebels by looking at the rebellion threshold in your country screen. You can also check each subjects loyalty by going to their country in the diplomacy screen.

Once they rebel, conquer them again separate peacing each rebelling country for all their land. Be sure to conquer the war leader last, as otherwise you might not be able to afford all the land in warscore.

For these guys, it's better to claim & directly annex rather than subjugate, unless you really want permanently loyal vassals. Just remember that it's very expensive to take land that belongs to the allies of the war target.

Aggressive expansion is probably the greatest limiter to expanding in Imperator Rome. For each point of AE, you get the following maluses:
-1% wrong culture group happiness
-0.5% wrong culture happiness
-0.02 claim fabrication speed
-0.5 subject loyalty (33 is the loyalty threshold)
FOR EACH POINT ABOVE 50 AE
-0.5% primary culture happiness
-0.1% monthly political influence
-6% aggressive expansion impact (this is a bonus)

Above 66 aggressive expansion, conquering new provinces is basically free. However it is nearly impossible to maintain this. Any foreign culture pops will have zero happiness, zero output, and max unrest. At that point, conquering any foreign cultures is just adding liabilities that will rebel in your country.

A pops base output is their happiness. A pop at 25% happiness will produce at 25% output.

Any pop below 50% happiness generates unrest. Unrest hurts religious conversion and cultural assimilation speeds MASSIVELY. If a territory is above 4 unrest it will stop converting/assimilating entirely. It also lowers provincial loyalty and outputs, but less significantly.

In short: high AE = low foreign output, high unrest = low conversion/assimilation speed

However it is possible to maintain low unrest with high AE, allowing us to circumvent the AE happiness debuff. Without going into too much depth, you can assign leaderless armies to a Region with the provincial army mechanic. Depending on how many troops you have assigned, every territory in the region can receive up to -5 unrest. This will allow you to convert pops to your primary culture, and in doing so significantly raise their happiness.

Note: it's faster to convert then assimilate pops, than it is to assimilate then convert pops.

If there's anything you feel should be added or that I missed, let me know :)

Thanks for reading.