"How about" are followed by nouns, clauses or Verb+ing. But is it grammatically correct to say "How about on Sunday?"
I got more results Googling "How about on Sunday?" than "How about Sunday?" Which is weird. Is there any grammatical explanation for this?
Grammatically, it is wrong to assume that a preposition should always be followed by nouns (or noun phrases), clauses or gerunds. It could be followed by a prepositional phrase. For example:
From behind the cloud appeared the sun.
In the above sentence, both "from" and "behind" are prepositions and "behind the cloud" is a prepositional phrase functioning as a complement of the first preposition "from".
In your example, "on Sunday" is a prepositional phrase which is acting as a complement of the first preposition "about". It doesn't have any grammatical issue.
Also, you could consider a gerund phrase (going to the movies) is omitted because it was mentioned before. For example:
A: How about going to the movies on Saturday?
B. How about (going to the movies) on Sunday?
You can omit "on" in the second sentence:
How about (going to the movies on) Sunday?
How about generally suggests a proposed answer to a question. To answer the question, when would you like to go to the museum, one could say either Sunday or on Sunday.
Therefore, one might also say how about Sunday? or how about on Sunday?
