Q. In “Who shall I say is calling?” is who the object of say (and therefore whom would also be acceptable), or is who the subject of is (and therefore whom is wrong)? I always thought one rearranged the order of the sentence to check (“I shall say whom”).
A. Who is the subject of is. When you rearranged the order to check, you stopped too soon: “I shall say who is calling.” I is the main subject, and shall say is the main verb. The entire phrase “who is calling” is the direct object of the main verb, shall say. (If you don’t trust your ear regarding who/whom, switch to a different pronoun and it may become clear whether to use the subject or object form: “I shall say she [not her] is calling.”)