Hi Cindy,
AtoM does not currently have a dedicated Maintenance mode or similar, but there are a few things you could try instead.
First, if your concern is about staff adding and modifying content mid-upgrade, AtoM does have the ability to disable login. See:
If you wanted your staff to have a way of knowing why they can't login, you could either add a maintenance message directly to the editable static area of your homepage, or possibly temporarily appropriate the customizable Privacy notification banner with a custom message. See:
If you are concerned about public users as well, one simple workaround would be to temporarily add HTTP authentication to the site, so no one can access your AtoM instance without the correct username and password. Not ideal but should do the trick. This is something that can typically be configured via your webserver - you should be able to find many resources online, but here are a few to start:
Additionally, I imagine it would be possible to create a simple local web page with a maintenance message for end users, and then configure a redirect via your webserver to that page while upgrading.
Finally, remember that AtoM's upgrade process does not typically happen in-place, especially with major version upgrades. Instead, the recommended process is typically to create a new installation alongside the old one, and then migrate the database and uploads/downloads directories. With that in mind, it should be possible to keep public downtime to a minimum, especially if the upgrade is run outside of typical business hours or during low traffic periods.
Good luck!