If you have multiple wonders do you get multiple special powers?
Each player has a single Wonder board, and each Wonder stage can only be built once.
The Quickstart rules cover this on the first page under Actions, but it is also covered in the main rules under Game Overview, Clarifications.  You may only build the stages in order from left to right, and each stage can only be built once per game.

build a stage of their Wonder(in the order given by the board, from left to right): the card is placed partially under the board, face down.
2.b. Build a Stage of a Wonder - [...] each stage can only built once per game. (page 5, main rules)

For example, if you have The Lighthouse of Alexandria, building the 3 stages of side (A) would give you 3VP, one Raw Material of your choice per build step, and 7VP in stage order. Building the 3 stages of side (B) would give you a Raw Material of your choice per build step, a Production Good of your choice per build step, and 7VP in stage order.