If I understand correctly, you want to install a patio awning on the curb side of the trailer, behind the existing patio awning?
Doing that will depend on whether you want to install it on the trailer sidewall or on the slide sidewall.
If you elect to install it on the trailer sidewall, when the slide is extended, you'll have some loss of area under the awning. It will only be possible to install in this location if there is enough space between the slide opening and the end cap of the existing awning. Keep in mind that with the slide cover in place, the attaching hardware for that cover roller extends beyond the end of the slide flange, so you'll need to make sure that roller hardware will clean the awning vertical arm of the awning you intend to install. That means you may need close to 12" or maybe even more space between the existing awning vertical arm/roller tube endcap and the slide cover awning hardware (mounted on the slide and extending beyond the side of the slide flange).
If you intend to install the new awning on the slide side, then you'll need shorter vertical awning arms and the awning maximum length will be limited to the length of the slide, minus the width of the flange endcaps and a couple inches for clearance from the existing slide cover hardware.
Short answer is, Yes, you can install a second awning on the side of your trailer provided you have enough clearance between the existing awning and the hardware attachment for the slide cover. The new awning vertical arm will need to be installed in the space between the existing awning and the slide cover projection. On some trailers there's not enough space, on some there is. You'll need about 12" if you intend to keep the slide cover AND the new awning.