There really aren't really class features between the Mage classes they share in mechanics or style. All the Sorcerer, Warlock, Wizard and other perspective mages classes share is Full Spellcasting and access to Arcane Spells. Since Bards have the same things, the mages might need something else to share to link them.
So here is my guess: Arcane Recovery
Arcane Recovery: Sorcery
At the 2nd level, you have learned to regain some of your magical energy by tapping into your supernatural blood. When you finish a short rest, you can choose expended sorcery points to recover. The amount of sorcerer points is equal to your half your sorcerer level (rounded up). Once you regain sorcery points with this feature, you must finish a long rest before you can do so again.
At the 8th level, you can do use your Arcane Recovery twice a day. At the 16th level you can do it three times a day.
Arcane Recovery: Eldritch Savant
At the 2nd level, you have learned to regain some of your magical energy by drawing on your pact. Once per day as a Magic action, you can recover one expended spell slots from your Pact Magic feature. Once you regain a spell slot with this feature, you must finish a long rest before you can do so again.
Arcane Recovery: Eldritch Master
At 20th level, you can draw on your inner reserve of mystical power while entreating your patron to regain expended spell slots. You can spend 1 minute entreating your patron for aid to regain all your expended spell slots from your Pact Magic feature. Once you regain spell slots with this feature, you must finish a long rest before you can do so again.
Arcane Recovery: Wizardry
At the 2nd level, you have learned to regain some of your magical energy by studying your spellbook. When you finish a short rest, you can choose expended spell slots to recover. The spell slots can have a combined level that is equal to or less than half your wizard level (rounded up), and none of the slots can be 6th level or higher. Once you regain spell slots with this feature, you must finish a long rest before you can do so again.
For example, if you’re a 4th-level wizard, you can recover up to two levels worth of spell slots. You can recover either a 2nd-level spell slot or two 1st-level spell slots.
Why?
So here is my guess: Arcane Recovery
Arcane Recovery: Sorcery
At the 2nd level, you have learned to regain some of your magical energy by tapping into your supernatural blood. When you finish a short rest, you can choose expended sorcery points to recover. The amount of sorcerer points is equal to your half your sorcerer level (rounded up). Once you regain sorcery points with this feature, you must finish a long rest before you can do so again.
At the 8th level, you can do use your Arcane Recovery twice a day. At the 16th level you can do it three times a day.
Arcane Recovery: Eldritch Savant
At the 2nd level, you have learned to regain some of your magical energy by drawing on your pact. Once per day as a Magic action, you can recover one expended spell slots from your Pact Magic feature. Once you regain a spell slot with this feature, you must finish a long rest before you can do so again.
Arcane Recovery: Eldritch Master
At 20th level, you can draw on your inner reserve of mystical power while entreating your patron to regain expended spell slots. You can spend 1 minute entreating your patron for aid to regain all your expended spell slots from your Pact Magic feature. Once you regain spell slots with this feature, you must finish a long rest before you can do so again.
Arcane Recovery: Wizardry
At the 2nd level, you have learned to regain some of your magical energy by studying your spellbook. When you finish a short rest, you can choose expended spell slots to recover. The spell slots can have a combined level that is equal to or less than half your wizard level (rounded up), and none of the slots can be 6th level or higher. Once you regain spell slots with this feature, you must finish a long rest before you can do so again.
For example, if you’re a 4th-level wizard, you can recover up to two levels worth of spell slots. You can recover either a 2nd-level spell slot or two 1st-level spell slots.
Why?
- Wizards already has it
- Warlocks already sort of has it in Eldritch Master
- People already complain that Sorcerers don't have enough sorcery points.
- Easy to learn
- Already Multiclass proof as they are based on class level
- Easy to tie Subclasses.