A possible workaround depending on your level of coding knowledge:
You could use the Transients API. Simplified: It adds an Option with an expiration time.
Then you could hook into the phpmailer_init-action and update the transient value with your new email. If the time expired, you could send the previously added mails out and then add the ones that are above 4.
Sorry, no code in detail as it’s more a server/hosting question than a wordpress one.
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