Consider the following example:
Er streitet sich schon seit Jahren mit seinem Nachbarn. (1.)
Here sich is singular. I would accept it (i.e. I would get the use of the reflexive form) if it were put in the following:
Er und sein Nachbar streiten sich seit Jahren. (2.)
Here sich is plural. What I do not get is the use of the reflexive form in singular when the reflexive action is clearly plural.
Wo wollen wir uns treffen? (3.)
To me this is fine. I do not meet up with myself (unless we are in some philosophy books where the ego can be split in several parts, allowing for the possibility of meeting up with oneself). I am meeting with another person=> We are meeting EACHOTHER (≈uns).
Yet, there is also this usage of the reflexive form:
Er trifft sich mit seiner Freundin um fünf im Park. (4.)
sich here is clearly singular. Yet the reflexive character of the action is clearly plural. If one wanted to use the reflexive form, one would have to reconstruct the sentence making er and seine Freundin the new subjects:
Er und seine Freundin treffen sich um fünf im Park. (5.)
To reiterate: I get the usage of the reflexive form in plural (like in (2.), (3.) and (5.)). I think that's quite straightforward logic. What I do not get is sentences like (1.) and (4.). Are they two different forms to say the same exact thing, or is there a (subtle) difference in meaning?
P.S.: I am not talking about the reflexive verbs where the action is singular (e.g. Ich wasche mich). I am considering on those where grammatically the verb is singular, but the reflexive action includes several people.