Old Fella
you are lookng at things entirely the wrong way. A single engined aircraft is designed to fly on... one engine.
A twin is designed to fly on two, but can continue on one in an emergency situation.
A Mayday can always be downgraded - the fact is ATC will be more concerned with the info you give them about the emergency than what prefix you use. ATC will then tailor the response to fit the scenario.
If a twin has a single engine failure, it doesn't matter to ATC if you call PAN or MAYDAY - the airfield emergency services response will be the same - based on the symptoms that the crew gives.
As far as ATC (certainly in the UK) is concerned, a PAN will give you priority and a no delay approach.
A MAYDAY will give you the same, but also allows the use of the non-operating runway.
As for someone who earlier said that unlike a PAN, a MAYDAY will mean that everyone else on frequency will say nothing unless called by ATC, that is wrong.
Normal service continues for other aircraft on the frequency, even if a MAYDAY is taking place. If ATC want you to be radio silent, they will tell you.
Although obviously affording an emergency aircraft priority, I always work on the basis that it is just another flight - to do otherwise is inviting myself to have an incident elsewhere in my sector because I am maybe getting too drawn in to one aircraft.