Antenna Mast - Picture
Yes, you can do it no problem. But USE GUY WIRES. As you can see from my pic, I used one set up near the top, and one down lower.
http://members.cox.net/mormandy1/Images/antenna mast.JPG
My mast has survived years of monsoons, sometimes with very high wind velocities. Once or twice a year, I go up and make sure the mast is perfectly vertical, and that all wires are tight. I have no doubt I could mount a much larger antenna with no problem, but in a high RF zone like mine, with most important things close by, the "sputnik" you see at the top works quite well for most things. The yagi is for one specific site, of one specific system by the way.
If you do not use guy wires, a 20'+ mast is going to do bad things in the long run.
Just as important, ground your setup properly.
My setup:
Antenna 40' above ground level. 12 mile line of sight to mobile radios.
Filed down to bare metal, at bottom of mast and used copper clamp to attach ground wires. Sealed the whole thing with silicone #2 (the good stuff). Each antenna has a static discharge block inline right before cables enter the home, and their ground wires tie into the main one. The main ground wire runs down to four ground rods spaced apart properly, all tied together, all tied to the electrical & cable & phone grounds.
All connections are sealed the same way. Silicone #2 doesn't shrink, or fall apart, or deteriorate in UV light.
If you do not ground your setup, wind moving across your antenna will cause static to build up, then discharge into the front end of your radio at some point, which ruins front ends, and makes them deaf to varying degrees, not good.
If a lightning strike occurs nearby, the energy in the air can do the same or much worse.
Oh and without proper grounding, you can burn your house down as well.
GROUND YOUR SETUP! DON'T SKIMP!