Is it possible to stack multiple protection enchantments on the same piece of armor? (an armor piece with both protection and blast protection, for example)

2 Answers

You cannot get two Protection enchantments on one item with vanilla enchantment or using books. You can do this using the /give or /summon command though (this command will give the nearest player iron leggings with Protection III and Feather Falling I):

give @p iron_leggings 1 0 {ench:[{id:0,lvl:3},{id:1,lvl:1}]}

Look at another answer to get more information how the command works.

The enchantment IDs can be found on the Minecraft Wiki.

No. A piece of armour can only have one type of protection on it in vanilla Minecraft. (Feather Fall on boots is not counted as a protection for this.)