I assume you're referring to a horn-hybrid example with a direct radiating, moderately efficient woofer section coupled to a high eff. horn ditto? And by multi-way do you mean actively? With a, say, 110dB sensitive midrange/tweeter horn obviously you can get by with very little amp power for prodigious output, whereas a woofer section of, say, 97dB sensitivity (still very eff. compared to the standard hifi speakers that barely exceed honest 87dB's sensitivity) requires about 20x more power at least for the same SPL. This leads many into a differentiated amp approach with low wattage tube amps for the top end and higher powered SS (often class D) variants for the lower bands, but to someone like me who's a stickler for coherency it's an approach that has negative impact here.
While I understand the want for wringing out certain qualities in the horn section with specifically "tailored" and lower wattage tube amps or other of particular interest, and with the rest of the frequency range being fed - it seems - more or less by power necessity and not much else, the summed output of these different "ingredients" makes for a less appealing sonic meal to my ears. The thing is though, you don't really notice it until comparing it with a scenario of using similar amps top to bottom, and by 'similar' I mean the same amp brand, series and overall topology that may have smaller variations in output power.
In my own 3-way actively configured setup I went from a 30W class A Belles unbalanced power amp for the midrange/tweeter horn section, an 800W (4 ohm) Crown K2 balanced class D amp for the mid basses and a +1.3kW LabGruppen balanced class D amp for the tapped horn subs, to essentially 3 similar MC² Audio class A/B amps - that is, 2x T2000 (625W 8 ohm) and one T1500 (575W 8 ohm), all of them fully differential balanced. To my surprise the slightly more powerful T2000 model sounded a wee bit better on the midrange/tweeter horn section; it was a wash on the midbasses why the T1500 ended up here, and the subs dug the T2000 over the T1500 a bit more.
Three different and incarnated audio nerd friends of mine have now listened rather extensively to my setup before and after amp swaps, and all them - by a mile - favor the MC² Audio powered system. One of them even expressed outright surprise to find the MC² Audio T2000 model bettered the class A Belles SA30 over the horns, to which I agree. I'm sure most audiophiles would assume, even downright proclaim without having listened to either scenario that the hifi brand 30W class A Belles SA30 amp (a great amp in and by itself) would trump the studio/pro segment 625W class A/B MC² Audio ditto in named context, but it just goes to show.
Why that much power for a horn-based setup, top to bottom not least? To me it was more or less about starting with the power requirements over the subs, which then led to experimenting with quite a few amps and learning how they affected the remaining frequency range. As it turned out the best full-range amp of the bunch (the T2000) also sounded best over the subs, which was then effectively "duplicated" to the rest of the driver segments on up. Who cares if you have close to a kW over a 111dB sensitive horn/compression driver combo when it's the best sounding combination? Prior to this experience I no doubt would have thought of this as being "overkill," as well as blindly assuming class A would - in general - beat a class A/B amp, but post experience tells a different story, and one that of course mayn't serve as an example for the same outcome in every other situation and context.
Sorry this got a bit out of hand, only to tell you that I wouldn't worry too much about power differentiation between a horn and woofer section; in fact I'd maintain what's effectively the same amp over the entire frequency range to aid coherency the best way possible, and if that means having prodigious power reserve for the very high eff. horns it's nothing to worry about. For as they say: headroom is your friend.