I would completely dismantle classes. With a limit of 5 boxes per bar, I truly believe game balance would survive in some form.
Tenesi Faryon of Telvanni - Dunmer Sorceress who deliberately sought sacrifice into Cold Harbor to rescue her beloved.
Hisa Ni Caemaire - Altmer Sorceress, member of the Order Draconis and Adept of the House of Dibella.
Broken Branch Toothmaul - goblin (for my goblin characters, I use either orsimer or bosmer templates) Templar, member of the Order Draconis and persistently unskilled pickpocket
Mol gro Durga - Orsimer Socerer/Battlemage who died the first time when the Nibenay Valley chapterhouse of the Order Draconis was destroyed, then went back to Cold Harbor to rescue his second/partner who was still captive. He overestimated his resistance to the hopelessness of Oblivion, about to give up, and looked up to see the golden glow of atherius surrounding a beautiful young woman who extended her hand to him and said "I can help you". He carried Fianna Kingsley out of Cold Harbor on his shoulder. He carried Alvard Stower under one arm. He also irritated the Prophet who had intended the portal for only Mol and Lyris.
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Order Draconis - well c'mon there has to be some explanation for all those dragon tattoos.
House of Dibella - If you have ever seen or read "Memoirs of a Geisha" that's just the beginning...
Nibenay Valley Chapterhouse - Where now stands only desolate ground and a dolmen there once was a thriving community supporting one of the major chapterhouses of the Order Draconis
I'd rather go with dusting up the old "secondary class" concept and let people add a new skill line to their existing three, say, after finishing cadwells silver or gold... might be new skill lines (stuff like "ranger" or "necromancer" or "cryomancer" or "druid") or it might be a cross-class skill line. Or even both, gain one after "silver", gain the other after "gold"...