Amp output versus Speaker imput


If I have an amplifier that is rated at 350 watts output - which I want to keep, does that limit me to speakers that have a recommended amplification of over 350 watts?

I'm in the market for new speakers and there are some I fancy but have a lower recommended amplification that what my amplifier is rated at. Do I discard these speakers or could I play them on my system but not turn up the volume too much. Or given the size of the room concentrate on high amplification speakers. I am budgeting about $16,000 to $20,000 for them.

My listening room is 31' by 10' for 14' then widens out to 15' for the remaining 17'. The speakers are placed in the narrow end of the room. I listen mainly to classical music.

Are there any recommendations that anyone might have on what speakers might be compatible?

Would truly appreciate anyone's input.

Thanks in advance
shiprepair
Post removed 
Almost every case of speaker damage is from too little power from the amp. While it would appear that if the speaker would take 100 watts and the amp was rated at 15 you would be safe, this is not the case. If you overdrive the amp you will drive it into clipping, which will eventually destroy the speaker. The rating is for continuous input, not music. I use speakers rated at, I think, 50 watts and use 300 watt amps often. In a recent test in HIFI News they found that a 500 watt amp worked well with a pair of bookshelf speakers rated at a fraction of that. The truth is these figures more or less meaningless. You can damage your speakers with an amp that is too large, too small or just right if you misuse it, with a little discretion you will be fine. As a classical listener your ears will give up far before the speaker is likely to. The important number is the maximum output of the speaker, if that number is higher than the level you listen at you will be fine.
1 watt of distortion can do more damage than 500 watts of clean power. You can never have too much. Keep in mind though that some of the best sounding amps made are only 3-7 watts.
This is one heck of a pair of speakers which ever they are. I echo the thinking that low power will be likely to do more harm than much more than sufficient power. I would think in terms of something that can comfortably deliver 700-1000 watts.
There are not a lot of amps that do this but McIntosh does have one that makes 2,000 watts. I don't have any idea of what it sounds like or what it costs.
In theory since I have not heard one in action, you can add a Musical Fidelity "supercharger" with either 550 watts each or 750 watts each. I think Audio Advisor has the 550s for a very low $995 close out price. That is down from $1995.00 which was at a heavily discounted price already .

MSRP I think was about $3000. It would appear to be a inexpensive option. It supposely simply adds power only to the signal you deliver claiming to preserve the sonic of your amp.
Musical fidelity products come from either the UK or China . I don't know where they make these. The English MF I am familiar with because I once owed a MF 308 amp. It was a very serious piece of gear that was very solidly built. I only sold it because I needed a more warmish coloration for my analytic, detailed Speakers.
Thank you all for your information. I'm a listener in the 85db class so my choice of speakers has been extended.

Thanks again