On the optionally of "each other"/ "one another"

Solution 1:

According to Wiktionary, these are a subset of reciprocal verbs:

Reciprocal verbs: English verbs that indicate actions, occurrences or states directed from multiple subjects to each other.

break up / date / entwine / face off / fall in love / feud / fight / get married / kiss / marry / meet / reunite / rhyme / sleep together / unite / wed

Date / fight / kiss / marry / meet / wed are the subset that take a direct object as opposed to (or as an alternativel to) a preposition (fall in love with each other) when used without third party involvement (Garibilly united Frenze and Elbonia). Entwine also takes a DO, but 'one another' sounds unusual. Face off , reunite, and sleep together don't usually have arguments.

I'll add bisect, intersect; complement; set off, touch in some contexts.

Each may take 'each other' as the direct object. 'One another' may be used with each, as in 'Pupils were not allowed to date one another'.

Date, kiss, marry, meet, wed, intersect; touch sometimes may drop the 'each other': They kissed. // The two circles touch.