Using a reputable third party bulk email service would be my suggestion.
Bulk newsletters and advertisement emails from your on-premise email server dont mix. We have a few customers like the one you describe. They are typically sales and brokers that need to advertise pricing info multiple times a day to a large amount of customers. We have told them repeatedly to stop using their business email to do this, because eventually they end up on block lists. They are also using MXLogic.
You can only control part of the problem on your end. Many recipients may be using gmail, hotmail, outlook, or other large hosted email providers. These providers are always monitoring their email traffic and it only takes one bad keyword, phrase, link, etc, in your email to trigger something on their end. Or if they are horrible at updating their bulk lists, and they send to invalid senders, even that can trigger a block. Multiply that by however many recipients are on the same provider and eventually you get added to a blocklist either by the recipients email provider or by a third party. Most blocklists are IP but some are domain based too.
Using a more reputable mail filtering service helps but only to some degree. We've also recommended things like constant contact but they never want to switch. But they complain all day when their emails get rejected and don't make it to customers. One thing i have thought of doing is setting up another SMTP server on the network with something like postfix with a different domain that they would use for bulk email and 1:1 NAT it with a different public IP, at least that way if it gets blocked, they can still correspond with other customers normally with their regular email addresses. Luckily it hasnt come to anything like that yet.