When multiple persons in your organization are sending marketing emails to your list, make sure that there is at least one person in the organization that keeps an eye on how frequent you email your contacts. Or at least agree on a maximum number of emails that you want your contacts to receive from you in a given time period. Then set up a calendar and mark who is sending what to which target group and on which date.
You don't need any fancy systems to keep track of this. Excel can do the job just fine.