Whether it's possible or not is currently unknown. It has not been revealed in the manga or the anime yet however other guilds will not let any wizard have 2 guild marks at the same time. This will question their devotion to the guild and it will be meaningless to stay in either of them. A guild is a family and you can only have one family.
It is arguable that the guild marks can be hidden under their clothes and nobody would notice. However some guild marks, like Fairy Tail's, is more than just a mark, it is a magic contract too as stated in the link you have given. It has not been shown that other guilds have them but it is possible to corrupt a wizard's magic with 2 different magic contract on their body. Just imagine 2 different natures of magic going on in a wizard's body.