Wow, I thought this forum was close to dead or that barely anyone posted here or something. Well, anyway, modding LOA would be an AWESOME idea! Perhaps activate any star you want, then build a colony there. Deactivate the mission scripts. That would be cool, if it's possible. Even better, someone making a mod that will randomly generate new stars and planets. Oh and yeah, it's possible to take over the whole Sol. Here are some images of proof.
Just a note though, I used the cheat where you can place any building in the game. But I used it after I took over everything, I swear.
(images are kinda big)
View of the Colonial solar system.
Titan (with a habitable atmosphere)
Io (with a habitable atmosphere)
You should try to maximize the fuel that is available. Then you should take over all American and European moons around Uranus and Neptune. You should have 3 fleets containing the best ships. Don't use defensive fleets, you can move your other fleets for protection. One fleet should be your massive "attack fleet" using up most of the fuel. The more you invade, the more fuel, so keep adding ships to this fleet! The other 2 fleets should have one of two frigates. After preparing, attack the Asian moons around Saturn. When Duna tells you to attack Hygiea, do it when you are safe from the Asians. Then go to Hygiea, and attack Mars like what Duna tells you to do, then you will have the tech, or Cruisers. Then you can improve your fleets. Attack the UEO moons of Jupiter. It takes a little while, but it's possible. These moons are high in minerals, you can use these to get even more fuel. When you are ready, move on to the asteroid belt, then mars. Don't attack Terra yet, you need all the ships you can get. Attack Luna, then Venus, and like the Jupiter moons, this planet is high in minerals too. Attack mercury, which should be easy. Then, when you're ready, attack Terra. This will take a while, so save, and keep starting the save file when you have the time or when you want to. You will be in for a surprise when you capture it. Colonies will start with a population of 6.4 billion, the main colony will be the largest colony in the game.
You may notice some buildings that you can't place normally in the game, these buildings do not do anything, they just use some power.
My brother fought and beat the UEO in exodus, but was kinda annoyed when Earth never came to colonial control.
Well, if you wait, and use top speed, it takes a while, but it will come into colonial control. It may take a while due to the shield generators.