Yes. It is called keying alike: every door is fitted with cylinders that open with the same key.
It is very handy in homes with several entrances, which is very normal around here: the front door, the patio door, the terrace door, the door from the garage into the house or the storeroom door. Instead of a bunch of keys, just one.
To do it, the locks have to take a European cylinder. If a door has an old lever lock, it can be converted to a cylinder first.
And it does not have to come at the expense of security: security cylinders can be keyed alike. If what you want is for each person to open only some doors, that is something else, a master key system. It is all in keyed alike cylinders.