Trak,
I think you are looking at the 'handling upgrades' question the wrong way round......
.... the 'upgraded parts' don't give it extra power, they allow the engine to survive at the inputs that the ECU demands.
So, lets start with the absolute basics (and I don't mean to sound at all condescending by starting at basics) - The actual lump(s) of metal that are bolted together to make the engine - well, Lotus already dictated a load of changes from 'stock' Isuzu lump to make it cope with a higher power and torque output - but it can still be taken further, if needed.
Personally, I wouldn't ever need to do anything like that, as what is already there is good enough for 350bhp, and to go to 450bhp the only thing I would change would be the head gasket (to a MLC unit)..... as these cars start to become undrivable once you get over 250bhp, not many people have the need to go higher.
Of course, there are always those 'left field' cars that go higher, but at that point it is not really a practical car for street use.
In 'OE' form the engine will make 165bhp (possibly slightly less on a FED car because of emission rules), and this is easily increased by fitting a 2 1/4" exhaust, allowing the standard engine to breath much better...... you will then be able to see ~180bhp.
An 'Everest' chip will allow the engine to develop ~205bhp
That is the point at which the other bits bolted to the engine become marginal - the turbo was selected to be small enough to give a rapid boost with little lag, but that comes at the expense of total airflow volume - so it will run out of puff not long after this point.... but before it does, there is a little bit more gain to be had from it.
Before you can increase the boost beyond the 0.92 bar "limit", you need to improve the fuel volume - the stock injectors run 325cc/min at full capacity, and once you go over the 0.92 bar boost, they simply can't physically provide enough fuel to prevent running lean, and engine detonation because of that.
So, with bigger injectors, you can then safely increase the boost level........ the standard turbo will go beyond 1 bar of pressure, but the MAP sensor will need to be changed at the 1-bar point, as the Elan uses a 2-bar sensor, but will then need a 3-bar sensor (1 bar atmospheric, plus 1 bar boost), but the turbo then becomes the limiting factor.
It is possible to fit a bigger/better turbo unit (Garret 2554R) but it isn't a bolt-in thing as it needs an adapter plate. All the development work was done many years ago by Lotusgirlmarie, and if you search the forum it will tell you how she did it all (and she did it properly!).
Of course, to control all that you need to change the ECU - this is where you can choose between getting the most out of it, and making do but keeping it useable......
..... to 'do it right' you would need to throw out the current ECU and replace it with a modern programable unit (Others have used Haltech or Microsquirt - I only have practical knowledge of Megasquirt from many years ago, and I'm sure things have moved on a hell of a lot since I last installed a unit on a car).
BUT
The thing is that the current ECU will work quite adequately if you use the simple maths (spelled for the UK, with the correct 's' at the end

) - if you increase the MAP by 50% (3-bar, from 2 bar), and then increase the injector volume by the same 50%, ie fitting 490 cc/min, it 'should' run the same - except it isn't quite that simple, as getting a 495 injector isn't possible, so the 'best' is a 550cc unit (easily available). This is why the programmable ECU will give a better end result, as it is infinitely variable for whatever you fit.
By this point, you will have maxed out the exhaust flow volume again, so will need to go to a 2 1/2" system, possibly with a custom downpipe (which would be needed for the turbo swap anyway).
After that (which can have you somewhere over 300bhp) it starts to get much harder, and the only Elan I've known to go above 400 was Costas' "Sh4rk" which is documented on the forum from 20 years ago, and got there using Nitrous Injection.
So, it depends on what you want to use the car for, and much of it depends on whether you want to follow someone elses ideas, or try to develop new ones - if I were to be building a pure track car I would use a standard engine, 2 1/2" exhaust, Garret 3554R, 3-bar sensor, Megasquirt ECU, 550cc injectors, oh, and fit a Quaiffe LSD in the gearbox along with a 3-puck clutch......
...... but if I "just" wanted a car to use on the road, with a fair few track days, I would stick to 2 1/4" exhaust, standard turbo, Everest chip and spend my money on good Yokohama AD052 tyres, Ferodo DS3000 brake pads and reduce the weight as much as possible.....
..... as it is, my car is built for road use, with (previous) occasional trackdays, and has the same as above, but with Yokohama 008R tyres, Ferodo DS2500 pads and I would empty the boot when I got to the track...... the limiting factor on track times was usually other people getting in my way, tyre grip, brake fade and running out of talent - not necessarily in that order!!!!
I never got to a point where I NEEDED more power, although I did get to a point where it may have made life easier.