The answer is yes, a Mason can belong to multiple lodges (I belong to three). But there are stipulations. A man will join one lodge at first. Once he has completed the MM degree, and is a Mason in good standing, then he is free to join other lodges, subject to the concurrence of his original lodge.
Some Grand Lodges permit their members to join as many lodges as they choose. Some Grand Lodges permit their members to join one lodge in their jurisdiction, and multiple lodges in other states. Some Grand Lodges permit their members to join only one lodge. The regulations vary from Grand Lodge to Grand Lodge.
Some men join two lodges in their community, and are active in both. Some men will take out a membership in another state, and cannot be active in a lodge that is hundreds of miles away.
If you wish to join multiple lodges, you should first inquire with the secretary of your home lodge, and verify the regulations with your Grand Lodge. If your home lodge permits plural membership, then contact the secretary of the second lodge, and ask for a petition of affiliation. Once the second lodge is satisfied that you are a Master Mason in good standing, your petition will be presented at a lodge meeting, and will be voted on.
The regulations vary from state to state. Some Grand Lodges require a petitioner to receive a unanimous ballot. Some require a 2/3 vote. Again, you should check the regulations of any lodge you wish to affiliate with.