Yes you can buy a 11.1 v, 5000 mah or bigger Lipo.
It is not the mah capacity of a bettery that determines the voltage, it is the number of cells connected in series.
BUT, your Sensei is designed to fly well with the battery it comes with. A larger battery as you are thinking of, you will get a much harder to fly airplane, because of the weight.
You may be able to find a slightly larger battery, but try to keep the weight as close as possible. A heavier battery will require the plane to fly faster to carry the extra baggage. You may not get much more time in the air, definitely not over twice as you are hoping.
Some batteries may have a higher C rating which means the internal resistance of the battery is lower than a battery with a lower C rating. I have had a startling difference in performance in a plane when I bought a higher end battery with a much higher C rating. My plane went from 170 watts to 260 watts just changing the battery. The lower C rated battery was not worn out, but I was almost at it's limit.
Instead of a large expensive battery, I would recommend buying 2 or 3 more batteries, then you can have almost endless fun.