How many PID loops could I run on cRIO RT?

Hi,
I am trying to create a temperature process controller. I have 3 RS232-enabled OMEGA mass flow controllers, 12 thermocouples, 6 heaters (that will be connected in sets of two), and 3 PWM-enabled fan banks.
My thinking is that I would connect the heaters in parallel to a phase-angle-fired SSR (http://www.chromalox.com/catalog/resources/PDS-PK308-SSR.pdf). That way, I could use a 0-20 mA output signal from the cRIO to control the power appplied to the heaters. I would use PID, and scale the output of the PID to a 0-20 mA signal to control the process temperature. I also want cascade control - I want to have 2 additional thermocouples that are connected to the PID loop acting as limit sensors. If the temperature limit is exceeded in either thermocouple, the PID loop is "turned off" until reset by a user. I would want three of these configurations (2 heaters, 3 thermocouples, 1 SSR - x3, so 6 heaters, 9 thermocouples, 3 SSRs).
Rather than control the PWM fans with a PWM output directly from the cRIO (which I heard can be painful) I found a PWM controller that is controlled by a 0-5VDC signal. I wanted to use a thermocouple as a process value, and the 0-5VDC signal would scale to control the fans to achieve the desired temperature. I would want three of these configurations (1 fan bank, 1 thermocouple - x3, so 3 fan banks, 3 thermocouples).
So now, my REAL question - Would one cRIO chassis be able to control these 6 PID loops AND my OMEGA mass flow controllers? I'm just unsure of the processing power that is required of PID/limit control.
I appreciate any help I get - If need any more specifics, please let me know!
Thanks!

Just to follow up - I have no problem using FPGA as well, if leveraging both the RT and FPGA systems will allow me to achieve my goal. I have heard, though, that FPGA is only good if you are only maintaining one set point for the PID loops. My fan bank PID loops will keep a constant set-point, however my heater bank PID loops will require constant changing (the heaters will be used to create a cycle that maintains one temperature for 60 mins, than goes to a different temperature for another 60 minutes, and repeats).

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