The final rise before it’s considered truly active is supposed to be 3-4 times the original amount, according to the Bread Bible.
If you’re starting off with 8 oz or so, and growing to 16 oz, then your culture is clearly active, although it might not raise the bread as quickly as you wish. If you want to experiment with it, you might add a bit of commercial yeast to the bread to increase the leavening. Allowing the bread to rise for too long a period might make it too sour.
The culture will grow stronger; you might consider increasing the number of feedings per day. I wouldn’t throw it out, since you’re clearly seeing some activity. What is the ambient temperature around the culture?