If you're lucky you'll have the sort of holesaw mandrel that has enough thread to take two blades, if so then fitting the original sized blade inside the new one allows it to act like a pilot drill would, stopping the new blade from careering across the ceiling.
You can get a twin threaded "pilot" drill thing that you put in the hole instead of the pilot drill. you can then use the say 60mm hole saw as pilost drill and then the larger one sit slightly back to cut the new hole size.
These are available in RS, only few quid and very worth it, used em a few times.
Look in the hole saw section, dont know what they call them tho, sorry.
Ross.
There is a machine available for your drill which has a plastic dome on it with foam around the edge and an adjustable blade to cut the hole. never used one but some people swear by them....or was that swear at them..LOL
I use one of these, especially when holes need to be enlarged. Very useful especially if drilling from below.
Purpose sized holesaw is quicker but dont drill from below.
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