The max level of PoE Awakened Gems is 6. The following example is an Awakened Greater Multiple Projectiles Support and the max level is 6.
Note that it is a corrupted gem. Corruption works the same as for regular support gems, sometimes adding or removing a level or up to 10 quality. Quality is hardcapped at 23%.
Using Vaal Orb to corrupt a PoE Awakened Gem, it has one of the following effect:
Note that it has risks to make a gem becoming worse.