This may be too much theory, not enough practical outcome, but...
You calculate the gain of a pentode differently than for a triode. The first tedious requirement needed is the transconductance of the tube at the operating point used. Once you have that, the gain of the pentode stage is the Gm (in mhos) times the a.c. plate load resistance.
Say you have a pentode with a Gm of 2000 micromhos and a 220k plate load resistor. Also say the following stage has a grid reference resistor of 1M. The a.c. plate load is not just the 220k, but because of the coupling cap, also the 1M in parallel with that. So that's 220k ll 1M or about 180k for our example. 180k * 2000 micromhos = 180k * .002 = 360. Much more than a single 12AX7 stage, but not as much as cascaded stages.
A helpful thing to remember is the meaning of the mho (or the british way to refer to it), which is current/voltage; that's the opposite of the way you'd write Ohm's Law for resistance. So 2000 micromhos is also said 2mA/V. 2 milli * 180 kilo = 360.
The a.c. load for all triode and pentode stages is always smaller than what you see for a d.c. loadline, due to the following stage's input impedance being in parallel with the load resistance. Except in a couple of notable cases... namely, when the following stage has a bootstrapped grid resistance like the split-load inverter, long-tail inverter and some variations of the cathode follower. We don't need to calculate the input resistance of these stages fully, just know that it is likely much more than 10 times the size of the plate load resistance. That means that when placed in parallel, there is almost no reduction of load resistance at a.c.
The implication of this is that as long as a pentode couples directly into the bootstrapped stage, and we allow enough current to flow through the pentode, you can use a large vale of plate load (like 500k, possibly more) to get even more amplification from the pentode.
There are limits, and a big trick is allowing enough current through the pentode, and ensuring there is sufficient output voltage capability to use the gain available. But it is worth knowing. For example, you could use this trick to get full output from a pentode into a phase inverter to output tubes with an input in millivolts to the pentode. The drawback is that you can't put a tone stack between the pentode and the phase inverter for the full potential gain. But you could have a triode stage and a tone stack/volume control, another triode if desired, and still be able to drive the snot out of the output tubes.