Add an Administrator account (or, for example, Company Administrator group) into Site Collection Administrators list for each of Personal (i.e. My) Sites at SharePoint Online instance.
Under the SharePoint Online tenant admin portal, you can go to User Profiles -> Setup My Sites. From here, you can add additional owners to new My Sites and set the secondary owner of the site collection when it is deleted. As noted above, this would only apply the admin settings to new My Sites after the settings are applied.
Adding an additional admin after the site is created is a little trickier but can be done by the tenant administrator.
The SharePoint Online PowerShell Management suite should be good enough to handle this task.
$tenant = "contoso"
$site = "user1_contoso_com"
$user = "admin@contoso.onmicrosoft.com"
Set-SPOUser -Site https://$tenant-my.sharepoint.com/personal/$site `
-LoginName $user -IsSiteCollectionAdmin $true