Expander PI with IO PI Plus

I have a project that is going to require a lot of IO. The program is actually quite simple and the PI can definitely handle it. But I need a LOT of IO. So here's the question:
Is it possible to use 3 IO PI Plus boards AND 1 Expander PI, AND still have access to the PI's 17 IO? From what I've been able to gather I can only use 2 IO PI Plus and 1 Expander or 4 IO PI Plus. There are ways I can make this work with a single RPi if the expansion boards will cooperate.
1- 3 IO PI Plus + 1 Expander PI + RPi 17 pins
2 - 4 IO PI Plus + RPi 17 Pins and some A/D circuitry on a couple of the pins.
I can reduce the number of discrete inputs by using more analog inputs but I'm hitting a wall there as well.
Ideally what I need is 64 discrete inputs, 56 discrete outputs, and 3 analog inputs, but I have some flexibility with the inputs. In some places I can substitute 1 analog input for 2 discrete inputs (travel limits) by using a motor with encoder or fitting the mechanism with a POT for position feedback.
Anyone know of a way to get that many IO from a single RPi?

The IO Pi Plus only uses the two I2C pins on the GPIO port while the Expander Pi uses the I2C and SPI pins. One issue you may find combining an Expander Pi with 3 IO Pis is the voltage level translator used on the Expander Pi I2C port stops working properly if the pull-up resistance drops below 5K. Each IO Pi has a 10K pull-up resistor on the I2C line so running three in parallel would drop their resistance down to 3.3K which is below the Expander Pi limit.

4 IO Pi Plus boards should work fine in parallel and will give you 128 inputs or outputs. You could combine this with an ADC board to give you the analogue inputs.

One way to increase the number of input pins would be to use multiplexers on the GPIO or IO Pi pins. Something like a CD4512BE or similar logic device would allow you to read 8 inputs using 4 pins effectively doubling the number of available inputs.