Like most things in life .......it depends!
Simple stuff you could have a go at DIY, then a garage with a ramp and a competent mechanic and a good set of tools could probably take a reasonable stab at say an oil service, including changing spark plugs (bit of a pain on a 911, but other than scuffed knuckles doable with a bit of patience), probably OK to change an alternator, various sensors, brakes etc.
BUT its finding the problem on a 996 that can be a real challenge, and a lot of money can be spent on fools errands. Even if its throwing error codes, you need a 996 specific diagnostic tester to really be able to understand them - don't let them tell you they've got a universal tester that can be programmed to read fault codes, because it will only be able to go so far - I've got a 98 C2, and the legacy tester for that is so specific, not all indy Porsche dealers have them.....!
If you want to get an idea of what a non Porsche garage might be able to manage I'd recommend the book 101 Projects for your 996 - bit of a DIY bible.
If you get to the point where you're needing to drop the engine down for any work, or separating the engine and transmission, I'd say you are automatically in specialist 'indy' territory.
So you pays your money and you takes your choice - or like me you pays lots of money and make some bad choices......then pay more money (see my take on the PORSCHE acronym below).....don't even get me started on geometry......Still, it saves on worrying where we need to go on holiday most years....[
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Where do you live by the way - there's indy's around the country, and Richard Hamilton can usually recommend someone reasonably local using his encyclopaedic knowledge....