Taking the Community down temporarily for maintenance?

It should be as simple as adjusting the Platform Visibility setting to offline. Then toggling it back when you’re done. 

I don’t see an option in the Customization > Phrases tool for customizing the message on that static page, but I’d bet there is a hidden phrase and/or support could help you edit it. 

If you click the ‘Offline’ option, the option to customize the text becomes visible.

Both @DannyPancratz & @TomW are absolutely correct.

It’s of course good practice as well to announce the downtime to your community members, letting them know how long the downtime will occur for and where else your users can go for engagement during its duration 😁.

The other piece of advice I’d have, is try to avoid keeping the community offline for longer than you have to. It can negatively affect your SEO if the search engine overlords cannot crawl the community properly and start erroring out.

Always test the changes first on Staging before attempting to make them live.

Oh - and ALWAYS keep a proper record of all the changes you make and back up everything before you start. Custom Scripts, Custom HTML and Custom CSS in particular are the sort of thing you will want to grab a backup copy of before you touch anything else.

If you have to rollback or abandon the changes, you’ll thank me later when you’re able to do so easily because you kept records of how everything was before you did the maintenance.