Can I use unpasteurized store bought miso to make more miso?
Maintaining a Koji culture is considered difficult, even commercial operations rarely do this. Meredith Leigh talks about it https://www.youtube.com/watch?v=4X-96_FFLyI&amp;t=11m35s
I think I may have read somewhere that the new Koji Alchemy book has good info on culture maintenance.
Most of my books on Koji don't even mention culture maintenance, although The Art of Fermentation by Sandor Katz does. It seems to be important to make sure there are plenty of nutrients. In Japan they add ash for this.

"When rice has cooled to body temperature, before inoculating, mix in sifted hardwood ashes, about 1.5 percent by weight of the quantity of dry rice you cooked. The ash provides potassium, magnesium, and other trace elements that promote healthy mold growth and sporulation."

Don't use white rice and do cook your substrate until it's quite soft.

Good luck!