So instead of finding and claiming a planet, you claim a star! A star would use a normal planet slot, and come in different colors and types (Red Giants, Neutron Stars, main sequence, etc).

Unlike a planet, a star produces nothing, and has only limited building space that can only be used on defenses. However, the star gives a passive percentage bonus that universally boosts some stat or production. The bonus should be small enough to not be game-breaking, but large enough to be valuable. For example:

Neutron Star
Size: Very Tiny
Space: 4
Bonus: +3% to total Scan

Blue Giant
Size: Mega Colossal
Space: 24
Bonus: +3% to maximum ship energy

Yellow Sun
Size: Very Massive
Space: 16
Bonus: +10% to all planet populations

Nebula
Size: Mega Colossal
Space: 24
Bonus: +5% to cloak

Black Hole
Size: Average
Space: 10
Bonus: +3% to attack
Penalty: -1% to maximum energy

Of course, you could have multiple stars of the same type, but they'd all be pretty rare to find, and would come with the sacrifice that they'd have no production. On the plus side, they'd provide a meaningful bonus that would scale with level.

There'd probably need to be a cap, like 'No more than 10% of your planet slots can be stars' in order to keep things balanced, and also make the choice of a star more meaningful.

stars are planets now are they?!

Nah, but it just seemed like the well was running a little dry for new planet types.

But there's lots of types of stars, and it'd add some variety. Besides, the premise of a Dyson sphere is that it's built *around* a star, so having a star in a planet slot isn't too far-fetched.

technically a dyson sphere isn't even supposed to be a complete sphere

and the star inside isn't necessarily the size of a normal star, the dyson sphere can contain a star that's been miniturised.

Aye,... "a black hole could be the power source instead of a star in order to increase energy-to-matter conversion efficiency. A black hole would also be smaller than a star."
-- http://en.wikipedia.org/wiki/Dyson_sphere

A dyson can be a shell too, just takes massive amounts of engineering and resources.