As an approximation, the available power increases rapidly with plate voltage. To give you an idea, here are three examples:
1) The stock quickie can generate about 1mW into a 4000 ohm load.
2) Using a choke (or series feed transformer) plate load into an 8K impedance, and re-optimizing the operating point, you can get about 4mW.
3) Running a 72v supply with a choke plate load and parafeed into a 5600 ohm output transformer, you might get as much as 25mW output.
These are three design point that I have worked out and can provide some details. A general rule for the engineering design of an amplifier is beyond the scope of a post or an article!
Notice that all the above degigns require an output transformer to match the optimum tube load impedance (4000 to 8000 ohms as above) to the headphone impedance (usually between 30 and 600 ohms). I am not aware of any ideal transformer to use for this application. Here are three less-than-ideal choices which have appeared on this forum in the past:
A) the "original" SPECO T7010. This transformer has not been available for a few years. It was used in earlier versions of the SEX amp and the Paramour, and those customers who upgraded the transformers had these left over; some of them used it with their Quickie. It can be wired for phones of 16-32 ohms and 300-600 ohms, but there is nothing in between. The bass capability is questionable.
B) the "new" SPECO T7010. We learned that the SPECO had been redesigned when an order came in with little tiny transformers instead of the larger ones we had been using. The new one was very different, which led to our use of our own design transformers for the amplifiers. This new one can be configured for use with the Quickie and drive any headphone, using four impedance taps. The bass is still questionable at least until someone tries it.
C) Our own OT-2 as used in SEX, Stereomour, and the Mainline headphone amp; only sold with the matching PC-3 plate chokes. Because of Quickie's low power, it is really only suitable for low impedance phones - less than 50 ohms. Very high sensitivity phones of higher impedance might work acceptably, but you'd need over 100dB/mW sensitivity to get even average levels. (Mainline has much more power and can drive higher impedance phones from its relatively low impedance output.)