You're not limited to one announcement — here's how multiple published bars behave together.

Yes, you can publish more than one

There's no limit on how many announcements you can create or publish at the same time.
Each one keeps its own settings — design, placement, targeting, schedule — completely independent of the others.

How they stack

Bars set to Top stack together at the top of the page; bars set to Bottom stack together at the bottom.
If more than one Top bar is also set to Sticky, the app automatically adds up their combined height so your theme's sticky header sits just below all of them — you don't need to configure this yourself.
There's currently no setting to manually choose which bar appears above another when you have more than one in the same position — it's automatic.

Each bar's own Z-Index setting still applies to that bar individually.
Running several announcements on the same page adds up in height — keep an eye on how much screen space they take, especially on mobile.
Use Placement, Device, and Geolocation targeting so only the announcements you actually want shown together end up overlapping on the same page.