I have a need to send emails out to around 4000 people. In the past I have used MailChimp for smaller mailings but they baulk at lists bigger than 2000. They even add up the total of all your lists to get the 2000 limit.

I have looked at alternatives like SendInBlue but they have even tighter limits.

Mailchimp is quite expensive to use their paid service as a monthly charge when I might not use it some months.

I am looking for suggestions of how to handle a mailing list of 4000 without it costing an arm and leg