An audio amplifier is (or tries to be) a voltage source. What that means is for any given volume setting it puts out a certain voltage and tries to maintain that voltage at it's output. Watts are then determined by the amount of current developed when this voltage is applied to the load (speaker impedance).
For example, let's use a 100 watt amplifer...
A 100w amplifer (driven to rated output) will have an output voltage of about 28 volts and produce about 3.5 amps of current into an 8 ohm load.
Because of the voltage source characteristics, that amplifier will try to maintain our 28 volt example even as the load increases/impedance drops.
Theoretically, that 100w amplifer should produce 200w at 4 ohms because our 28 volts applied to a 4 ohm load results in twice as much current as it did at 8 ohms, or about 7 amps. Some amps with large power supplies and or regulated power supplies will do this and "double down" as it's often referred to. However, most won't because of the current limitations of the power supply.
So, what happens to most amps is that they reach a point with increasing load where the power supply cannot produce enough current to maintain the output voltage. When this point is reached, the output voltage begins to sag, and as a result the "double down" effect is not observed.
Going back to our example, the amp could produce 3.5 amps of current with the 28v output @ 8 ohms resulting in about 100w. But, for sake of discussion, let's say it's power supply couldn't produce the full 7 amps of current necessary to maintain 28V and double down at 4 ohms. However, it's power supply could manage 6 amps of current at 4 ohms. This would result in about 24V and an output of approximately 144 watts - which is not at all unusual for most amps to have 30-50% more power at 4 ohms compared to 8 ohms. Of course, some may be more, some may be less.
Usually, at 8 ohms and higher, the output limitation is voltage related based on the power supply's rail voltages. As the impedance drops/load increases, the output limitations become the inability of the power supply to keep increasing current to maintain the rail voltage.
Keep in mind there is a lot of fluff when it comes to talking about "high current" amplifers. Some mfg, such as H/K, cite high instantaneous current specifications. Unfortunately, these don't mean much in the real world because the impedances used for these measurements are extremely low; short circuits, essentially.
Prepare for sidetrack...
For example, the H/K 3385 stereo receiver (rated 85wpc @ 8 ohms) claims 42A of peak current. I don't doubt it's ability to do that, but it won't do that at any normal (or even most abnormal) speaker load. And, you can't force more current to the speaker than the voltage and impedance dictate.
That receiver will develop about 26V and 3.25A to produce it's 85w rated power at 8 Ohms. People see the spec saying 42A of peak current and never really look into the math and assume it's going to do that with THEIR speakers. Let's say your speaker is rated 8 ohms, but drops to 4 ohms at certain frequencies; not unusual. Well, 42A @ 8 ohms produces 14,114 watts and requires 336 Volts to get there, if the impedance drops to 4 ohms, it requires 168V to get that 42A and results in 7,056 watts. I think we can see that isn't going to happen with a 85wpc amp or receiver that has a rail voltage of probably around 40V, give or take.
Since the receiver's power is spec'ed at 85w I'll give the benefit of 3dB headroom resulting in 170w peak (at 8 ohms). On this assumption, 42A of current could be developed if the speaker impedance dropped to around 0.1 Ohm.
I don't mean to disparage H/K gear, it's fine stuff. They just happen to provide the numbers for a good example.