I think comestay sounds weird because it juxtaposes two verbs. Come to stay sounds more 'natural', at least to me as a Londoner.
Also come and stay works because of the separation of the verbs by the conjunction.
Your come stay sounds poetic. There isnt any grammatical reason not to express yourself this way as far as I can see.
Perhaps Dave will correct me if I'm wrong, but I'd say that "come stay" is fairly standard in the USA, whereas it sounds strange to the British ear.
I'd include the and to conjoin the verbs. I don't know about the other 311 million Americans, but I don't think it's that prevalent. Hearing "come stay" (or "... sit," "... stand," etc.) makes me think of an imperative with a comma between the verbs:
Come, stay here.
I might use it with the dog--she doesn't obey, though! However, this isn't the case with marie's example.
[...] I think visiting grandma is different than visiting with grandma in that the latter includes interaction, like conversation. I can visit London, a museum, or the library, but I can't visit with those.
Okay, I can see your point, Dave, and it's probably as plausible or (il?)logical as mine or others.
However, for me, native Aussie, visiting with always first implies / paints a picture of visiting someone (else) in the company of (the with part) another someone -- the person named.
I visited with my sister (on my own perhaps, but not specified; similarly perhaps at her home, but not specified). "Foreign" to my sense/s.
I visited Mother with Aunt Mabel. (I went to see Mother with Aunt Mabel, perhaps at Mother's residence.) Not ambiguous because the visitee (Mother) is named.
I visited with my sister. (I visited [someone / some place 'understood' or previously identified] with my sister. "Natural" looking / sounding statement to my senses -- assuming context / storyline has introduced the visitee ahead of the visited with.
I'm sure the with has seemed foreign to my receptors "forever" in the style you describe, Dave. But our Ozlish socio-culturo-linguistic mindset-cum-lexicon ... is quite a potpourri of our primarily UK- English roots, post-WW / other "lesser" wars imports from Other-Anglo cultures / lexicon ..., international distribution and availability of Other-Anglo media (spoken / written), "our own" slang, idioms, styles, and cultural perspectives / legends that subtly (or not) influence or expand our AU English.
Each English-language-based nation's lexicon is also influenced by its unique NESB migrant intake programs.
P'raps it's just another little example of peoples' being "divided by a common language".
Another, of long standing, springs to mind: the US-AU English difference over fanny -- to an American it's an innocent synonym for buttocks / ass but in Oz it refers to the female pudenda and remains toward the less publicly acceptable, more "offensive" euphemism for that anatomical feature. I've witnessed a US (theology) student innocently offering his solicitations to a young female Aussie student who had slipped, fallen, and landed on her rump; the poor young gent was rewarded with a strong and indignant slap! He soon learned that lexical variation! ;D
PS: No, they didn't go on to marry and live happily ever after.
We have a thing here called a fanny pack, small purse-like thing with a belt that's fastened around the waist. Most users, though, seem to have the pouch positioned in the front for easy access, not on their (US) fannies.