question

Hi @fsdg-2871

What are the limits?How can I increse limits?

These limits are throttling settings to limit a mailbox from receiving too many emails in a short period of time.
It is intended to ensure that other mailboxes can receive emails without problems.

To increase the limits, you may follow add these two keys to the MSExchangeDelivery.exe.config file (default location: Program Files\Microsoft\Exchange Server\V15\Bin)
By default the values on Exchange 2013 should be:

 <add key="RecipientThreadLimit" value="3" />
 <add key="MaxMailboxDeliveryPerMdbConnections" value="8" />

You may change the values to increase these limits.

Do I need to increse limits on organization level or server level?

In my opinion, if a server is hosting specific mailboxes which need to receive many messages at a time, you may need to increase the limits on the server.

Is there any official Microsoft document? If it is on server level is it same for Exchange 2013,2016 and 2019.

Sorry I didn't find some related documentations which have more detailed information on this topic.
Here is a link with the similar question for your reference: Probling with Throttling of Emails by Exchange 2013 servers

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