If you want to stay with Porsche sanctioned tires, those with the N numbering system, you need to go online to the Porsche site and find the options/accessories area and see what tires are recognized by Porsche for the wheel size you have or want to use with your model/MY vehicle.
I believe what you'll find is for a 20" wheel while there are a few different tire brands to choose from the sizes will be the same.
To get a higher profile tire I believe -- I haven't bothered to look this up -- you will have to go down in wheel size to a 19" or even maybe down to a 18" wheel. This of course assumes an 18" wheel would fit, is approved for use on your car and if you like the looks, etc.
If you elect to move away from tires with the N number system -- which I don't recommend -- visit Tirerack and search for tires that will fit the wheel size you are interested in and pick a tire that has the higher profile. Get the right speed rating, tread wear, load rating to be as close to the same as what a similar Porsche tire would offer in these areas.
Be careful. If your car came with different size wheels front and rear or same wheel size but different profile tires front and rear be sure you keep the size/profile relationship the same. If you go too far afield this can possibly cause problems with the car's ABS, traction control, stability control systems. (Tire speeds can become to different from each other or what they should be from some baseline and an error message/warning light may appear.)
In some cases -- if the car is AWD -- the front and rear profiles can be different to cause the front and rear wheels to turn at slightly different speeds. This was the case with my 996 Turbo. The wheel size was 18" all around but the front tires were just a little taller and made fewer revolutions per mile vs. the rear tires which because of their profile were shorter and made more revolutions per mile. This difference in tire revs per mile caused a viscous clutch system between the rear axle and the front axle to heat up and in doing so caused a special fluid to become hotter which caused it to became more viscous and the faster spinning rear axle driven discs in the coupling transferred -- via fluid friction -- some torque to the discs connected to the front axle and this is how torque was routed from the rear axle to the front axle and how the car's AWD system worked. The amount of torque transfer ranged from 5% (at I do not know what speed) to 40% at above 150mph.
If you stay with the same size wheels but find higher profile tires that otherwise work (fit, don't rub against anything; but how to know they'll not rub under say full suspension compression and at the front with the front wheels turned is beyond me) the speedo will read wrong. Not sure if this will affect the odometer's accuracy (my Boxster's speedo was approx. 5mph optimistic -- this with a factory installed set of 17" wheels/tires fitted instead of the factory base 16" wheels/tires -- but I confirmed the odometer was accurate) but as I touched upon above it might cause a problem with the car's traction control, stability control, possibly even the ABS. Whenever one chooses to go off the reservation from what the automaker sanctions/supports there is the risk of complications.