Gogar has it right and so does Rusty. Sure, just about any speaker is rebuildable with just a few ex exceptions. I decided to pass on a pair of Altec 824A speakers on our local CraigsList because the horn tweeters are made of unobtanium and not rebuildable. But yeah, most paper cone speakers can be rebuilt. If you are building a system around gobs of power, there are lots of choices. Thousand-Watt amps are readily available. More complex speaker systems (3-way, 4-way, etc.) are less efficient, so more power is required. More efficient speakers are louder at a given power level. The decibel scale is logarithmic. A 104db speaker is way louder than a 94db speaker. Multi-way speakers are going to be inefficient. mid-80s or lower. So you need more power. The relationship is interesting.
Doubling the power to a speaker increases loudness by only 3db. Most people can hear this increase in loudness, but just barely. If you multiply power by 10, loudness is doubled. So.....a 1000-Watt amplifier is twice as loud as a 100-Watt amplifier.
There are so many ways to skin this cat. Last week I ordered an amplifier kit and a preamplifier kit to build. These are vacuum tube devices using a "single-ended triode" topology. The power amp makes 8 WPC. That's not a typo. Candidly, you'd be surprised what one Watt can do. Yup. One single Watt. All of my other vacuum tube amps use a "push-pull" topology. The PP monoblocks in my living room right now make just 12 Watts, and this is plenty. My speakers are 89db sensitive and those 12 Watts are actually driving two pairs of speakers! So yeah....you'd be surprised at how few watts are actually being used when you listen to music. My PP tube amps sound great, but I heard a couple of single-ended triode amps recently and the difference was striking. Like lifting a veil. Like the band is right there in the room. Seriously.
At any rate, I am moving in the absolute opposite direction from the OP. There is nothing wrong with high powered systems. I am choosing simplicity. In fact, one of the biggest improvements I have made to my hifi system recently is to remove the preamp from the signal path. That's right. No preamp at all. My sources are connected directly to my power amps. There is a switching device with a volume control, but that device is ONLY a switch. No tone controls. The improvement in sound quality was striking when I removed the preamp. Here are the monoblocks I am using right now:
