Women do it all the time, but the appearance of a high density is much less of an issue with them.

It's possible if you keep your own hair short and go with a longer full cap, but it isn't going to work if your existing hair is long, especially if you are attaching a shorter style full cap. If I remember correctly Andy who used to post here ended up switching to a full cap after he wore one for an acting gig. He posted a pic and it looked great.