Replace 12mF with 47 mF caps in PSU. Good idea or not?

Bad idea as it will not improve matters just stress the transformer and associated components in the power supply. If 33 or 47 would have been preferred, Philips would have used them!
 

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I concur with Jon. Its a bad idea to increase the value.

If the originals are the cause of your hum (have you proved this by further diagnostics?) then replace with similar value or if you can not get 12k then fit either 10 or 15k but no more.
 
It didn't hum when new.

If it hums when old, put new parts in.

12mFd (12,000uFd) seems like plenty for most power amps. It's not exact, 10m or 15m would be fine.

But 4X the value does look excessive, maybe risky.

If I build a garden shed, and the plans call for 12cm (4.7") rafter beams, and I put in 48cm (19") rafters, I lose headroom (ouch) and increase stress on the walls. It would take a greater depth of snow, but snow on a small roof can only pile-up so deep.