Like facebook sometimes says, "...it's complicated". If the operating voltage is where you want it, you should be able to get a bit more voltage out, compared to stock. But I haven't checked how the voltage tracks with varying battery voltage, and the difference between tubes and as the tube ages enters in as well.
If you want the biggest possible headroom, you should use a plate choke, and adjust the bias as well. The Hammond 156C has been popular; a 2K bias resistor will bring the current down for more symmetrical clipping - you might see 9v fresh, 6v depleted batteries.
This is a great way to explore the meaning of operating point analysis. Find the Sylvania spec sheet for the 3S4; it's the one than has the triode-mode curves. Since the voltages are so low, you can experiment all day with no risk of damaging the tube (which is cheap anyhow, if you get experimenter-grade tubes!).