The Half-Breeds: Half-Ogre, Half-Rakshasa, Half-Minotaur, and Half-Dwarf

Just like half-elves and demontouched, there has been no definitive explanation on how they are born, and half-breeds sometimes spontaneously appear in the Dragon Empire, although not always to the delight of their parents and communities.

Simple Reflavoring

For GMs who want a quick and dirty conversion that doesn't require the features below, feel free to reflavor the Dwarf, Dark Elf or Half-Orc into either the Half-Ogre/Half-Giant or the Half-Minotaur, the Dwarf into the Mul, , and the Half-Elf as the Half-Rakshasa.  For those who want more distinct mechanical differences, see below.

Also, in keeping with the theme, the following half-breeds already exist in 13th Age: Half-Dragon (Dragonspawn), Half-Fiend (Demontouched), Half-Celestial (Aasimar) and Half-Drow (Half-Elf).

Half-Ogre/Half-Giant

+2 Strength OR +2 Constitution
Ogrish Toughness: Once per battle as a quick action, you can spend a recovery to gain temporary hit points equal to the rolled result.

(Champion Feat): One battle per day when you trigger Ogrish Toughness, add 1d6 per level damage whenever you miss with a melee basic attack.

GM Note: Notice that the Half-Ogre/Half-Giant and the Earthborn/Stone-Touched both share the same benefits for their racial power.  If you wish to use both races, but want to make the Half-Ogre/Half-Giant different, replace the Half-Ogre/Half-Giant's Ogrish Toughness with the following racial power (racial feat stays the same):

Monstrous Strength: Once per scene when making a Strength-related check, you can choose to lower the check's DC by an amount equal to your Strength plus the current escalation die.  You can do this even after finding out the result of your check.

The reason why I didn't want to make this the default racial power for Half-Ogres/Half-Giants would be because it doesn't feel "right" for me to grant this strength-specific power to them.  But if that works for your campaign, then so be it.

Half-Rakshasa

+2 Intelligence OR +2 Charisma
Shapechange: Once per scene as a standard action, you can change your form to that of any humanoid. While shapechanged, you retain all of your statistics, and you can turn back to your own form as a standard action, although being reduced to 0 HP also forcibly turns you back to your own form.
It takes a successful hard save for nearby creatures to notice that there's something... different, about you, and other factors (like trying to mimic a particular person, acting out of character, or trying to look discreet) that could make the save normal, easy, or impossible (GM discretion).

(Champion Feat): Whenever a creature trying to determine if you're what you look like rolls a 5 or lower on their saving throw, you can change it to a natural 1 and improvise on how their attempt to see who you really are actually works in your favor.  Perhaps they expose useful information about the creature you're trying to appear as, or they can even become friendly to you (until they find out who you really are).  The better the storytelling improv, the better the result, though if the GM thinks your suggestion is going too far, they can enforce a smaller version of your improv or call for an unmodified d20 roll (high roll likely gets what you want).

Note: This race easily works for Changelings and the like.

Half-Minotaur

+2 Strength OR +2 Wisdom
Goring Charge: During your turn, when you make a melee attack a staggered enemy you were not engaged with at the start of your turn, add damage equal to your Strength modifier on a hit.  Increase this damage to twice your Strength modifier at level 5, and three times your Strength modifier at level 8.

(Champion Feat): You also pop the enemy free from any other creature they're engaged with except you, and they have a -2 penalty to disengage checks against you until the end of their next turn.

GM Note: This is the only race I would design to overlap with the Barbarian's Slayer talent, and generally benefit from a charge-like ability.  This is due to the iconic nature of the Minotaur's goring charge.

Half-Dwarf

+2 Strength OR +2 Constitution
Half-Dwarf Endurance: Once per scene you are able to perform strenuous tasks for longer periods of time.  This will usually come in the form of lower DCs for one Constitution check, but may also involve other activities that can put significant strain on your character, such as heavy lifting or hurried tome-scribing.  Discuss with your GM how this feature works during character creation.

(Champion Feat): Increase the number of recoveries that you have by one, and the first time you rally each battle can be done as a quick action instead of a standard action.

GM Note: This is a rather tricky thing to resolve mechanically, but for those who are more familiar with D&D's Mul race might have an easier time with this racial feature.