To increase refine rate of Solid, Wicked, Precision Weapons between +9 and +11 by one, you need to use a Clock Tower Refine Hammer (101390) with 1000x Lead (1000680) and 150x Clock Gear (1000681) .
The Clock Tower Refine Hammer (101390) can be obtained from Goblin King MVP in Clock Tower Unknown Basement or purchased from MC HAMMER in (paramk 30, 30) (not accurate, he moves around) for 150x Lead (1000680) and 30x Clock Gear (1000681)