You're still pulling from the same power supply. That is the issue.
Using the FTC's 5 rules* established in 1974 (which is generally what we mean when we talk about amplifier maximum clean output power levels in watts) passive bi-amping still gets you nowhere in terms of "increased output"
even if you use two, independent, monoblock power amps each with its own, independent power supply.
In my example in my AVS forum post I linked to earlier the maximum output levels of that particular amp at 20 Hz and 200 Hz (which are just two of the many frequencies the amp needs to be able to successfully excite over its claimed bandwidth of 20-20kHz) are:
255.1w for 20Hz, when presented with a 4-ohm load at that test frequency
and
267w for 200Hz, when presented with a 4-ohm load at that test frequency
both when driving just one of its amp channels into the standard 4-ohm resistor
@gene used for his
measurement of a Denon AVR amp channel into a 4-ohm load. [see figure 5 at the link]
[I selected 200Hz by the way because this speaker exhibits 0 degrees phase angle at that frequency.]
OK, but what happens if we buy a secondary amp of the exact same model, for "passive bi-amping" purposes (so we are effectively using two independent monoblock amps each with their own, independent power supply) and just drive the woofer section alone? What will the maximum output at the 20Hz and 200Hz test frequencies be then? Will they improve because this amp is no longer "burdened" with the tweeter section?
Well that's easy to determine by examining how the impedance load presented to the amp changes in this new two-amp scenario by disconnecting the jumper straps and powering the speaker's woofer section all by itself. Now the amp only sees the woofer section load but is freed from the burden of the tweeter section load. Let's examine how the load changes at those two test frequencies by looking at the posted impedance curve of this speaker when you connect to both woofer and tweeter together (top image, CONVENTIONAL single amp scenario) vs. only connecting its woofer section all by itself (PASSIVE BI-AMPING load scenario, bottom image):
Measured impedance (Y-axis) vs. frequency (X-axis) of a single amp connected KEF speaker, by "AJ in Fla":
[Added text by me, m.zillch.]
Measured impedance (Y-axis) vs. frequency (X-axis) of a woofer section
only KEF speaker, by "AJ in Fla":
[Added text by me, m.zillch.]
Sure, there are all sorts of changes in the overall impedance curve the amp sees across many different
higher frequencies but when outputting just isolated 20Hz and 200Hz test tones by themselves, the ones in question, the load the amp "sees" under
both scenarios (one amp driving both woofer + tweeter sections vs. one driving just the woofer section alone) stays at exactly the same value in both diagrams: 4-ohms. [My green arrow only points at 20Hz so you'll have to inspect what happens to the measured impedance load at 200Hz using your eyes on your own

.]
If an amp experiences no changes in the input signal frequency nor the load it is faced with when driving that isolated test tone frequency (20Hz and also 200 Hz in this case) then its maximum output power when playing those two isolated frequencies,
does not improve/vary. If the maximum output power does not grow at either 20Hz nor 200Hz, as I've just demonstrated, then one can't claim passive bi-amping has "higher output from 20-20kHz", under the FTC 5 rules, because both of those test frequencies fall within that stated range of its claimed output power.
*The FTC 5 rules advertisers had to stipulate back then (when amps were usually only 1ch or 2ch) were:
1) How many of the amp channels are being driven simultaneously? [It's easier to drive one channel instead of both.]
2) Over what specific range of frequencies do you claim your amp can provide this level of power? [20-20kHz being typical but not a rule. They can state different ranges but they must declare it].
3) What is the impedance load the amp sees at all these test frequencies? [8-ohm is the most common, followed by 4-ohm]
4) How much permissible THD do you allow at this claimed output power? [ <1% and <.1% being the most common values chosen.]
5) Is the claimed output level continuously sustainable over, say, 5 minutes? Or is it only momentary for breif peaks in the signal? [Amps can "cheat"" by stating their peak output which in truth they can only attain for a fraction of a second. Continuous output is more important and more strenuous (although having good peak capability is a good thing too).]