I have had the back break out in a corner driving onto the motorway once. Brand new tyres, but that does not help much. There just is loads of grip right untill you get to the limit and then it is gone.....
There area few points to make here if I may. First you say they were 'brand new tyres' but I hope you had run them in for around 300 kms at low speed first? Brand new tyres always have some of the coating still on them that allow the tyres to be easily released from the molds, and this makes them slippery. The running in process at low speeds should get rid of all that whilst also allowing the carcase to settle properly.
Since they were brand new tyres, if they weren't exactly the same as you had on previously, then you should always treat them with respect until you have learnt how they perform and grip, because different tyres will have different characteristics.
Next, it is really important that the Murena has the correct tyre pressures on them, especially the rears, and if you are running standard wheels and tyre sizes then the front should be 1.9 bar but the rear MUST be 2.4 bar for a 1.6 or 2.5 bar for a 2.2 model. If the rear tyres are less than these then it will break away more easily than it should.
Also a mid-engined car has a low polar moment of inertia, which should give it a higher cornering capability than other types of layout (front engine rear drive, or rear engine rear drive) but one inherent trait of a mid-engined car is that when it does break away, it snaps very quickly! It will also snap-oversteer if you lift off suddenly when cornering quickly, so that should be avoided at all costs. Always bring the speed down before entering the corner and power through it, increasing the power as you exit.
Finally, if/when you change wheel and tyre sizes for something different, you need to check the relative tyre patch size and adjust the pressures accordingly. Bigger tyres does not necessarily mean more pressure. It might even be less.
Roy