Hi HuntWorks,
Welcome to this Apple (user-to-user) Community!
Re: Trying to set up custom domain email address : We’ve been trying for several days; same error :
“This email address is not available. Please try again with a different address.”
and “Something went wrong. Try again later.”
Am no expert in his area, yet your post to the community deserves some response.
To sidestep issues that arise: It is wise to keep the OS versions up-to-date with the newest compatible version on all Macs and devices.
Else:
Restarting a Mac or device can often help restore order if something is not working as expected.
(Deletes temporary files, re-establishes connections, may update recent setting changes, and more.)
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Re: "All other email accounts for family members have worked just fine. What do we do?"
Wondering if your customer domain can support those new e-addresses.
Apple Support's online article (link below) may help find the solution:
See how to: Personalize iCloud Mail with a custom email domain and share with others - Apple Support
Eg: says:
" Send and receive email from a custom email domain
You can use your iPhone, iPad and iCloud.com to add an email domain
and share it with up to five friends or family members.
You can either purchase a new domain or move one you already own to iCloud.
If you already have email addresses at a domain, you can configure them and assign them to others during setup. Otherwise, everyone can create email addresses later.
Each person can have up to three active email addresses per domain. The domain owner can also decide to accept emails sent to addresses that aren’t actively set up with the domain. Because your custom email domain uses iCloud Mail, it works in the same way. When you configure or create a new address, you can automatically send and receive email from that address in Mail anywhere you have iCloud Mail turned on, including your iPhone, iPad and Mac.
You can also access your mail in Outlook on a Windows device and in a web browser at iCloud.com.
Note: Mail stored in iCloud counts toward your iCloud storage. If you run out of iCloud storage space, you won’t be able to receive new emails at your custom email addresses until you make more storage space available."
Also: Send and receive iCloud Mail on all your devices and keep Mail settings up to date - Apple Support
Eg: says:
"Keep Mail settings up to date
When you turn on iCloud Drive in iCloud settings, you can also store your Mail settings in the cloud. This way, you can keep your mail signatures, VIP contacts, Smart Mailboxes and more up to date on all of your devices. The settings that stay up-to-date depend on the device you’re using"
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If needed: You may want to reach out to iCloud Support:
(There is a "Get Support" link (online chat, phone, etc) at the bottom of their webpage (link below):
iCloud Support Website:iCloud - Official Apple Support
All the best :-)