"Come over" and etymology of other idioms
I think that this is one example (well, pair of examples) where an analytical approach is better than an overall view - looking at the semantics of the preposition over, rather than treating 'come over to' as a lexeme best considered opaque. (I'll have to bite the bullet and treat over as an intransitive preposition in these examples.)
Kota Kodachi, in 'A Study of Prototype Formation of the Meanings of Prepositions...' at http://www.paaljapan.org/resources/proceedings/PAAL10/pdfs/kodachi.pdf , looks at the semantics involved in the various senses of various English prepositions, suggesting a logical hierarchy that the senses fit into. Though he majors on the prepositions at, in and on, I'll suggest an analogous treatment of over.
One model illustrated, put forward by Tanaka, is that prepositions have:
a central (prototypical) sense which is spatial (locative or directional);
a less central looser spatial sense;
non-spatial (in the geometric sense) senses.
(Other models differ; temporal usage may be seen as an alternative prototypical usage.)
Illustrating Tanaka's model with on:
on the table / floor
on the bus / train
on time / on the hour / on fire / on tenterhooks / on good terms with / on the pull ...
It could be argued that a three-point scale is not adequately differentiated - does 'on television' come in category 2, 3, or somewhere between?
On this model, over in come over to is the less central looser spatial sense:
1a. over the lake (= above the lake)
1b. over the lake (= from one side to the other)
1c. over the river (= on the other bank)
2 not 1. go over [the intervening ground] to see someone
3 not 2. Brazil's victory over Spain
The best overall treatment of fixed expressions (including idioms) that I know of is
Fixed Expressions and Idioms in English: A Corpus-Based Approach by
Rosamund Moon