Are you asking what will happen if charged particle meets a beam of non perfectly coherent and polarized light?
You may see such examples in plasma being opaque, if dense enough and also early universe being opaque due to distances and amount of charged particles.
Particle will interact with incoming photons and randomly change direction, with average force being close to zero. Each time charged particle changes direction it emits a photon, that weakens the original one and amplifies the one that goes sideways, where charged particles was moving.
If you ask how specific direction can be selected as preferred one for emitting photons, you may want to check this device:
If you ask how specific direction can be selected as preferred one for accelerating electrons, you may want to check this device, the one with RF:
If you ask about reference frame of photon, then its not meaningful. It has no time, from it prespective it did not react with anything other than the target electron, immidiately after being emitted by the source.
If you ask about popular images of photon that shows spin or polarization when it hits the target, its not useful in your question. Electron doesnt see this complex pattern, for it photon is a simple object that makes one force, depending on polarization and phase on impact.
If you ask if photons can interact with each other, answer is usually no. Only through gravity or matter creation for extremely high energies.
If you ask how to go in calculations from one photon to many photon beam: consider that only polarised and coherent part of the beam pushes the electron in the same direction. So, if beam is 23% vertical polarisation and 77% horizontal polarization, consider that 46% (smallest, 23% multiplied by 2) of the beam is scattered and 54% is useful in polarization. If 12% of the beam has phase of 0 deg and 88% has phase of 180deg, that is unlikely, but easier to calculate, then part that is scattered is 24% (smallest part, 12% multiplied by 2) and 76% is useful in phase. In total 76% of the beam being useful in phase and 54% is useful in polarization. 76% multiplied by 54% is 41%, and this part of the beam acts as one strong photon, pushing the electron in the same direction. The rest of the beam is wasted, pushing the electron in random directions.