Having the largest customer base in the market sounds great, but you need to know more. Customer satisfaction is one of those things. This may sound basic or obvious, but I'm amazed at how often I have seen this overlooked - myself included.
When conducting due diligence on Company 'X', ask what service aspects they believe their competitors are poor at and what differentiates customer satisfaction at Company 'X' from the comptition.
Then ask to see the results of the most recent customer satisfaction survey they have conducted along with the results of previous surveys. This will give you an idea of what direction they are heading in. If the most recent survey is too old to be considered useful, ask for it to be conducted again and compare results with a previous one. If one has never been conducted, ask for one to be put together and sent out. Also ask that you may review it before it is sent out.
In both previous or newly created surveys look for questions that address the answers to the first questions posed in this article: what is the compitition poor at and what differentiates. If the survey doesn't address these then ask why.
If a company's customer base is about to walk out the door, you would want to know this before acquiring them or investing in them.