I had an idea in line for this:
NQ Lvl 45+ weapon would give good odds at a grade 4 materia
HQ Lvl 45+ weapon would give great odds at a grade 4 materia
Weapon with Grade 3 materia "hells fist" would significantly improve chances of similar family/color materia being created.
The above effects can stack.
Furthermore, I believe the following should be allowed:
Spiritbonding a Sarrnga (for example) could guarantee a heaven's eye 4, which can be bound to a future Sarnga.
