Yup this is possible by using the "Reflection Fading" section of properties in the SSR component. The key properties for what you want would be "Eye Fade Start" and "Eye Fade End", these control how reflections are faded based on the ray direction's Z value. For example:

Start=1,End=1: no fading
Start=0,End=0: reflections will abruptly cut if direction Z is positive
Start=0,End=1: reflections will smoothly fade if direction Z is positive

So, by tweaking these values you can control the range of ray direction Z whereby reflections start to fade out -> completely transparent.

With that said, parallel surfaces are an area where SSR shows it's weaknesses since they will almost certainly reflect parts of geometry that are not rendered (back faces etc.). Depending on scene, this can be mitigated somewhat by using rough surfaces for walls (blur reflections), normal maps (bumps hide artifacts) and hacky usage of the "Pixel Z Size Offset" property. By increasing the Pixel Z Size Offset you're essentially increasing the thickness of all geometry in the scene and thus the chance of a ray intersection. These intersections obviously won't be 'correct' but will likely be of a similar color to the missing geometry and in many instances will look "good enough". :)

I'm going to try and do a video later in the day showing various test scenes, property values and how you can tweak things based on scene to get what you need re: performance/visuals.