Cat aggressive with other cats in the house

We've got three cats. One we've had for 10 years, the other two are brothers who are now three years.

The 10 year old kitty has never been a fighter or a hunter, she's just happy to have a home. The one brother is the same - he's a big good all whose greatest catches are moths and lizards.

But his brother is the most aggressive cat I've ever had. He's the sweetest angel to humans and to the dogs, but to other cats? He's constantly in fights (there are a lot of cats in our area and fights often happen in our own garden too, it's not illegal nor uncommon for cats to roam). He never goes further than one house away, the cats often come here and our house (rented) can't the altered to keep cats in and out.

But he's even a bit rough to his brother, and full on tries to fight (occasionally, not often) with our 10 year old cat.

As I type this he's purring away on my lap, making mini meows but I want him to calm down. Will a hormone or calming supplement work?