Getting another female is indeed a good idea. I like to keep at least three females per house, and as a rule they all get along. You will first need to quarantine the new one, though, so if there are any existing health problems, they are not passed on to the mice you already have. If you cannot put the new one in a separate air space, keep her in another room with a door you can close. Push a towel under the door for extra protection. (In case you think I am being a fanatic, I am not. Many viruses are very contagious and air born. Respiratory infections are notorious for spreading quickly amongst the mice houses.) Three weeks is the recommended quarantine period.
When you are ready to start the introductions, do it in a neutral area. Make sure there are no items with the scent of any of the mice around. Wash any accessories you plan to use in the area, so they do not smell like any of the girls. Bathtubs, beds with sheets covering them or large, clear bins are common places people use to introduce the mice. Allow the girls to roam and sniff. As long as there is no blood drawn, a few squeaks here and there are not a concern. If the two older girls are ignoring the new arrival and going off on their own together, you may need to start with one-on-one introductions. Allow one of the older mice to spend some alone time with the new arrival, and then switch and put the other older mouse in to meet the new one. You should again wash all items you are using, so the older mouse does not smell her friend and spend her time looking for her rather than meeting the new girl. Continue this process for at least a week. You should also begin swapping items between the houses. Take something with the scent from the one cage and swap it for an item from the other cage. It will get them all used to each other's scent. You can even swap houses. Put the new girl into the other mouse house, and the other females into the new girl's place. Also, keep the houses next to each other. If they are wire cages, make sure they are far enough away so the mice cannot take a swipe at each other through the bars, but have them close enough so they know they are near. When you feel comfortable with how they are behaving, begin a meet-and-greet with all three in a house that has everything scent-free. Wash the house and all accessories very thoroughly before putting all of the girls together; nobody can claim an item as theirs, so to speak. A little arguing may ensue at first, but again, as long as there is no bloodshed, there is no need to worry. Observe the mice to see how they are interacting. If the older ones are ignoring the new arrival, put a dab of vanilla on all their rumps. It masks their scents and makes them all smell alike. Do this meet-and-greet for a couple of times to really get them used to each other. It is a lot of extra cleaning for you, but in the end you will be thankful. When the extended periods of time together have proven successful, you are ready to try putting them together for good. In the 15+ years that I have been doing introductions between many, many mice, only twice did it not work out. Two females just did not want to get along with anybody, so I was forced to house them alone. For further ideas to help with the introduction process, TFM is a wonderful mouse site with a wealth of information on anything mouse related. Following please see their section on "Introductions":
http://www.thefunmouse.com/info/introducing.cfm
They also have a mouse cage calculator. It will help you determine X amount of space needed for X number of mice. The link can be found at:
http://www.thefunmouse.com/info/cagecalculator.cfm
Having an extra cage on hand should the need arise is a smart idea; however, the odds are in your favor that the females will have a successful introduction process, and you will have a happy colony of mice. I wish you all the best with them.