I think you'll find this problem isn't so easy to analyze or solve. What you have are not spatially separated beams, at least not in the sense that there's a beam of signal going through those specific areas in your window.
The reason is the same reason why individual atoms can't be imaged by an optical microscope: diffraction. Anything small relative to the wavelength of light (or RF radiation, which is just a much lower frequency of light) can't be resolved.
So what you are observing when you stick your antenna in the window and get good reception there isn't that you've placed the antenna in a "beam". Rather, it's just in that particular spot, you've just happened to find a local maximum in the diffraction pattern.
The orientation of the antenna also plays a role, since unlike visible light from the sun or an ordinary light bulb which is incoherent radiation, radio radiation is mostly coherent. This means (among other things) it has a particular polarization, and if you don't match that polarization with the antenna, you'll experience signal loss.
This diffraction pattern can be perturbed by anything with electrical properties different from free space anywhere within a few multiples of wavelength. Unfortunately this means it's not feasible to design an antenna that will "catch" all those signals. Remember they aren't really beams anyway. Simply adding an antenna will perturb the system.
My advice? Trial and error, just as you'd adjust a TV antenna. There's no guarantee you'll find one antenna and orientation that works well to receive all the signals.