Can I wire 1 more bluetooth antenna to extend the range?
..put 2 antennas on the same wire ...Will it work?

No it won't as antennas need to "see" the correct impedance (usually 50 ohms)  in order to work properly. By simply adding an antenna in parallel you disturb that "characteristic impedance" and the will actually make the antennas less efficient so things will get worse.

Won't the signals be caught by 2 antennas interrupt each other?

No it does not work like that, but it will definitely not work for the reasons I explained above.

For a proper 2 antenna solution there need to be two antenna connections present on the PCB. And even then, it can be that only one connector is physically connected.

If there is an antenna connector on the PCB you could possibly use a better antenna. You can use a WiFi (2.5 GHz) antenna as Bluetooth uses the same frequency band.

But ultimately, Bluetooth isn't designed to work well through (concrete) walls so your goal of being able to extend the range so that you can cover multiple rooms is simply a bridge too far for Bluetooth.