The arithmetic is simpler than most teams assume. Take your target sends per month, divide by the working days you actually send on, then divide by the daily volume you are willing to put through one mailbox.
Conservative operators keep a single mailbox between 20 and 40 sends per day once warmed. Pushing higher does not usually improve pipeline; it compresses reputation and moves the whole domain closer to the spam folder.
That gives you mailbox count. Domain count follows from how many mailboxes you place per domain — spreading identities across more domains limits the blast radius when one gets flagged.
The cost consequence is why the platform choice matters. Per-seat platforms scale cost linearly with mailbox count, while domain-priced infrastructure like Azure lets you add identities without adding per-seat spend.
Model it before you buy, then order in one batch so all mailboxes finish warming on the same schedule.