Your best bet would be to either get a large SD card, or use the USB 3.0 port on the keyboard dock for an external hard drive. The Transformer came from the factory with either 32 or 64GB solid state drive(SSD) and one SD card slot. ASUS has said the SSD was not field upgradable. That's not to say it couldn't be done, but getting that tablet opened without voiding the warranty could be a challenge! There's a web forum dedicated to the ASUS Transformer line that proved to be very helpful to me, and they might be able to offer guidance as well.
Asus Transformer Tablet Forum