Naturally Aspirated tuning:
The H6 engine (especially the second generation) is already a powerful engine, with over 80HP / liter power output.
One area that the engine is lacking is the design of the exhaust headers. The first generation EZ30 had a single exhaust port on the head, which impacted free gas flow, but was required for the engine to meet its emission standards (the purpose of this strange exhaust port arrangement was to get heat in the catalytic converters as soon as possible).
The second generation engine (EZ30R) had a revised head design, with 6 exhaust ports. This was a significant improvement, allowing the engine to breath more freely, but unfortunately, Subaru still had to design a convoluted exhaust manifold design, due to emission regulations again. While the exhaust headers look good from the outside, the headers are actually of a three-layer design with significant airflow restriction.
The exhaust design is the one area that can be easily improved on this engine. Custom, or tuning headers, like the OBX H6 headers can gain significant improvements:
The ECU of these engines is easily tunable, and can even be tuned remotely, by companies such as XRT Tuning.
Further gains from this engine in Naturally Aspirated form are hard, expensive and the results may not be satisfactory.
There is more power that can be extracted at the top end, but since the engine is usually installed in large and heavy cars (as the Legacy/Tribeca), to gain a significant power boost, large improvements in torque are required, which cannot be easily achieved with a naturally aspirated engine. Furthermore, lack of good aftermarket tuning parts is going to make any such project hard and expensive.
Turbo-charging the engine
While turbo-charging any engine not originally designed in this way is an expensive undertaking, it is quite cheaper than NA tuning, especially in terms of HP per dollar spent.
With stock internals this engine is known to be able to cope with 400+ hp and 0.5/0.8 bars of pressure. The usual turbo choice is the Garrett GT3582, or some of its clones.
The stock plastic manifold needs to be replaced in any case usually with a custom manifold.
In any case, this engine is known to have insufficient cooling capacity, so before commencing any modifications, an upgrade of the cooling system is required.
Supercharging the H6
Supercharging the H6 engine is a popular project, and there is a kit you can buy to make the conversion itself. – The Raptor Supercharger kit.