Recommendation letters: The more the better?
Does the strength of an application get enhanced by containing more recommendation letters?

Not necessarily. Having too many recommendation letters can overwhelm the person reviewing your application and it may leave a bad impression of you in a couple of ways. One example is you do not know if the the reviewer will go through all of the letters that you provided. This may lead to the reviewer not being able to have a clear picture of who you are, what is your work ethic and how driven you are (these are just some general examples of what a reviewer could be looking for). Generally, most applications ask for 2-3 letters of recommendation. 

What if the additional letters are coming from less-related (to the field that one is applying for) staff, but impressive enough?

If it doesn't specify what kind of letter you need to submit, the letters of recommendation that you think will help the application the most is the ones you should send. If you are still unsure, you can call them and ask how many letters of recommendation people usually send them.