In high-energy particle accelerators, we have limited possibilities for what kinds of particles we can collide due to their charge, radiation properties etc. I understand that in LHC we collide high-mass particles such as protons or lead nuclei because they are electrically charged so we can use electromagnetic methods. They are massive as well so their radiation output is not that large as well.
Is there a possibility to attach some emitter of different particles like electrons or neutrons to some of the detectors "from the side" to have new kinds of collisions on high-energy? (True that it would be still only 6.5 TeV collision and not full 13 because emitter would not have its own accelerator, nevertheless we could then have the possibility of neutron-proton collisions and many others.)
Is it technically difficult or even tested to collide particles perpendiculary to the synchrotron beam?
Is or why wasn't this scheme used in the construction of LHC?