My name is Unknown - stray!

This kitty showed up in our yard ~10 days ago, got into yowling contests with our feral male Siamese named Simon. We did not want another feral but thought Simon might like company; however, within the past few days the stray has become very aggressive toward Simon and chased him away. I moved the stray into our 3-season room with a radiator, so he/she (gender unknown) has been warm and has eaten all food provided (very hungry), but our house is tiny; Simon still sees the stray and only stays long enough to grab some food. The stray is otherwise friendly, walked into the house and does not mind being picked up/held, likes belly rubs, etc. and purrs quite a bit. Seems very much like a former indoor cat that either wandered off or was dumped. I took to the vets to scan for a chip (negative) but otherwise have not had any health checks done and again gender is unknown. Seems like a good potential only cat, or maybe with other cats (seems to like our pup too) in the right situation.