I've been asking for something familiar since i started back in ARR 2.0 and it's so easy to implement that im going insane over it.
Everyone thought (in my circle atleast) that the minimum ilvl mode was gonna be the big entry to this, but no. It never happend sadly.

It doesn't have to be harder difficulty of the dungeons even, just challenges in their current state.
I use this example as i've used countless times but i try to keep it short.

Hullbreaker Isle
Basically you could have an achievement where you have to beat Sasquatch in the minimum ilvl mode without ever feeding him one banana.
Beat Sjoorm on minimum ilvl without taking bubbles
Beat Kraken on minimum ilvl without allowing him to drag his tentacles back into water
Beat Hullbreaker Isle on minimum ilvl in 15 minutes or less.
That's 4 achievements for 1 dungeon. Earning all 4 could reward you a specific title related to Hullbreaker Isle.

Now you could expand this and have 4 achievements for each dungeon there is and make bundles.
Complete all challenge achievements for all the heavensward lvling dungeons (51-59) to earn a "Heavensward lvler veteran" title or something silly
Complete all challenge achievemnts for all lvl 70 stormblood dungeons to earn a mount or a token that you can exchange for an exclusive glamour to the class you want. To make it flexible you can trade the glamour to other classes whenever you wanted by exchanging each piece to an npc vendor.

The dungeon+ idea is cool and all, but i feel the simple "make it harder" is so outdated. There's so much potential in this tho and they are doing absolutely nothing, it's sad. Because dungeons only require 4 people and there are no new heavy mechanics involved, it's stuff you already know about. You just have to figure out way to deal with the challenges. It would be challenging content that would fit anyone, casuals or hardcore.

Even more simple. Make timed dungeons alone. Beat dungeon x on minimum ilvl in less then 13 minutes to achieve gold, 15 to achieve silver, 20 to achieve bronze.
Get bronze in all dungeons of stormblood and you get an achievement
Get silver in all dungeons of stormblood and you get an achievement + mount
Get gold in all dungeons of stormblood and you get an achievement + exclusive glamour