The receiver should not be a problem, but the transmitter has to be specific for RTS. All this transmitters have a 433.92 MHz frequency (RF), but RTS use a 433.42MHz frequency.
With a RF transmitter it will be almost impossible for you to control yours sunscreens.
On the other hand, if you have a RTS transmitter, you can control the RTS devices and almost certainly you can also control the normal devices (the RF ones).
I started just like you, and I could barely control a cover in the same room. With a RTS transmitter I can control 3 RTS blinds and 2 RF devices distributed between 4 rooms.
What I did was buy an STX882 transmitter and replace the oscillators with a 433.42Mhz from ebay.