Could someone get a manmade enamel layer put onto their teeth?

Porcelain: If you are asking about a dental veneer, yes. It is make out of porcelain, not actual enamel, and it usually covers the buccal and incisal or occlusal) surfaces of your teeth.

Lots can be done: See your General Dentist. There are many esthetic restorative solutions available today that look great, are long lasting, and are amazingly life-like.

Sort of: While not as good as natural enamel, the tooth can be covered partially with a porcelain veneer (laminate) or completely with a ceramic crown.