Sure enough, it's true! He comes in holding a box, opens it, and takes a ratty old wig out of it, without having to put the box down!
Now, another prevailing theory is that instead of arms, he has limited telekinetic powers. This might seem to suggest that possibility, allowing Homestar to manipulate an indeterminate number of objects at a time. But on the other (invisible) hand, it's possible he has three or more arms!
In conclusion: Cartoons are fun and weird.