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In Elgg 1.9 or newer there's the maintenance mode you can enable in the admin section. With maintenance mode on only admins can log in.
Being difficult I am still using 1.8.15 :D
Then you can try it with this plugin: https://elgg.org/plugins/794641.
Be careful with upgrading Elgg to a newer version while the maintenace mode is on. I don't know if it works with the plugin. But if I remember correctly the older Elgg versions at least (in your case "newer" as it started with Elgg 1.9 that a maintenance mode was in core) had a problem with executing the upgrade script with enabled maintenance mode. You could end with the situation that not even admins could log in. I don't know if the problem still exists in the latest Elgg 2.3. Maybe it has been fixed by now.
Thanks iionly! Very helpful as always.