I believe that Boeing currently produce eight 777s a month. When the 77X comes along there is no reason that they could not ramp up to this level given the demand is there.
777 is currently at 8.3/month - 100/year. Rumors that they might try to increase that to 10/month in the future (they just loaded the first 787 body section at the 10/month rate).
There will likely be some disruption during the transition from the current 777 to the -9, I'm sure within a year or so of certification and initial deliveries they'll be back to at least the current 8.3/month rate.
One open question is, if they build the 777X other than Everett, will they rob the fuselage tooling from Everett, or duplicate it? If they decide to go elsewhere and duplicate the fuselage tooling, it would give the capability to continue to build -300ER/200LRs, while at the same time creating the -8/-9 capability elsewhere. That in turn could eventually turn into the capability of two 777 productions lines with capability of ~16/month if the demand is there
