Can we have solar facing three directions with only two inverter input channels?

There can be specific requirements about your install which need an experienced designer but one that many qualified solar installers don't realise is that there is a trick to make a two channel string inverter work very well with 3 inputs.

It's perfectly acceptable to have arrays facing different directions in parallel to the same MPPT tracker. The only proviso is that the arrays are electrically balanced (usually equal numbers of the same module) and the inverter in question can handle the current input.

Fronius even wrote a whitepaper on it. 

SE_WP_Advantages_of_east-west_systems_EN.pdf

In many instances one input can have an east and west facing string, the other input can cover your north facing array.

You might also consider an Enphase miroinverter or Solar edge optimised system that is even more flexible and quite scalable, but bear in mind that whatever you install this year will likely be superseded in 5 or 10 years so adding capacity or redeploying existing modules may not be particularly feasible.

 https://www.solarquotes.com.au/blog/how-to-upgrade-solar/

This attached shows a house I did many years ago, 7 panels face east, 7 face west and these are connected in parallel on the same MPPT. The North array also happens to be 7 panels but could be a different size or different type of module on the other MPPT. 

For another example, this very unconventional system has a single input inverter with a notoriously difficult, narrow input window. It was arranged with two completely different arrays with three strings in parallel.

By the numbers there is a string of eight modules with a 12amp & 18 volt nominal output, so they supply 144 volts to the inverter at maximum power.

The other array consists of eight panels with a 5 amp 36volt nominal output, these are wired in two strings of four modules, for a similar total of 144volts. 

Despite being totally different solar modules from different manufacturers, they're well within 5% variation and so can be used efficiently on a single inverter input