Portable Holding tanks

Hello,

I have a Montana High Country Fifth Wheel and am permanently stationed on private property.  My electric, water, etc is all hooked up through my families water/electric lines.  I currently have a company coming out about every 2 weeks to empty my tanks, but of course that is getting pricey.  

I'm curious if there would be any issues if I were to purchase a portable 300 gallon holding tank to store underneath my RV,  hook it up to the emptying valve, leaving all 3 tanks (Black and grey) open.  So every time I would use the toilet, shower/sink it would all just flush into the portable tank. 

I am not located near a dumping site, so my only option is using a porta potty service or finding another method of dumping.

Any guidance on this matter is appreciated.