This is possible with the Ascension spell.
The Ascension Spell states:
You imbue a number of creatures with mythic power, granting each of them 1st tier in a mythic path of its choice. The creatures immediately gain the benefits of their chosen paths. Divide the duration evenly among all targets.
This allows us to select the 1st-tier Archmage path ability Flexible School which says:
Select one wizard arcane school that is not your arcane school. You gain powers from that arcane school, treating your tier as your wizard level for the purposes of these powers. Once you have chosen the arcane school, it cannot be changed. You cannot select an arcane school that is one of your opposition schools.
You must have the arcane school class feature to select this ability. You can choose this ability up to three times, each time selecting another arcane school other than your own.
However, despite this adding another school, you will only be considered level 1 for that school.
There is no other way (that I could find).
The extensive list of Feats including Third-Party ones, does not include the equivalent of Eldritch Heritage for Arcane Schools. Going through the different classes, including third party and prestige classes, there was nothing listed that would give two Arcane Schools with a single class.