Answer

When you gain a card from a location with a stacked pile, you only take the top card of that location. The cards underneath remain at the location, maintaining their order.

This is supported by the following rule:

• "Gain the top card of a location that you did not deploy to this turn, then gain that location’s bonus."
  (Page 3)

There is no mention of taking more than the top card, and the rules specify that you may always look through the cards on each location, but they must remain in the same order. Thus, the cards underneath stay at the location until they become the new top card and are gained in a future action.

Source: page 3.

Source: Core Rulebook (pp. 3, 5, 6)