The level does not increase.

AhnaldT101 provided  all the possible sources currently available.

Everyone got five for free.

Four are awarded from Tier 4 of the Marquee.

Episode Pass awards three 

Pass Plus awards a bundle that has another five. 

Tier 1 R5-D4 $30 shard pack gives two. 

Tier 2 R5-D4 $100 shard pack gives seven.

26 total upgrades and you start at level 1 so Era Loaned Level 27 if all are applied. 

Currently only way to lvl theloaner units is if you purchased packs that included something to lvl them.