Is there a maximum number or data size for e-mail messages transferring to Mac Mail via imap?

I am dealing specifically with migrating cox.net e-mail from cox imap servers to yahoo imap servers and setting up the MacOS Mail application. Due to a variety of other complications with this specific use case, I am wondering if there is a glitch preventing a large portion of the messages from downloading to the computer, or if there is a just cap on how many messages or how much data is allowed to be synchronized via IMAP. 

I am dealing with an account with an exceptionally large mailbox. 13K+ unread messages in the inbox alone, and perhaps as many read messages. It’s a very old account. After successfully moving the cox.net e-mail address to yahoo and configuring the Mac Mail app to send and receive, the mailboxes were populated/synched over the course of the day and night, but only show about 5K unread and 9K read messages. 

I compared the Mac Mail inbox contents to the Yahoo webmail inbox by sorting first by newest first, and then by oldest first. The inboxes appear to include the same date range overall; it isn’t that the mail app only downloaded the most recent 9K messages. So. I haven’t yet figured out what messages are missing. With so many messages it is not going to be easy to look for what’s missing by just looking back and forth at both lists. 

To clarify, the messages are theoretically all accounted for in Yahoo webmail. At least, the quantities listed at the top match what the old Cox account had before the migration. But a huge portion of those messages are not being synchronized to the Mac Mail app. 

It would help if I had information about any limitations on Yahoo’s imap servers. 

I have no reason to question the settings for the e-mail servers. The account can send and receive new mail. I was even able to move a message from a different inbox (a different address configured in the same Mail app) into the Cox/Yahoo Inbox. Yahoo threw a warning that it could be nefarious since it was not added through yahoo’s mail servers, but it moved successfully and synchronized to the webmail inbox as expected. 

The issue seems to only involve existing messages from prior to the migration. I have no clue yet whether there is a pattern to what has been omitted since I haven’t figured out what’s missing. 

Is anybody else trying to migrate excessively large inboxes? (And please, don’t bother recommending a purge. That is in progress. The user is not ignoring the issue; it just takes time. I’m not seeking mail management advice. I’m asking for information to explain why not all of the messages are synchronizing to the Mail app from yahoo.)

thanks for any help you can offer. 
cheers.