I looked a bit into it.
Unfortunately JBL does not let me browse the us website but they do have some nice subtle looking speakers:
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When looking at Watt Ratings you need to look at the RMS rating, not the peak/music power rating.
What does it help if your engine makes 500hp but only for 1 second otherwise it blows up?
Your aftermarket stereo has the following specs:
Information for the KD-T910BTS. JVCKENWOOD's product information site creates excitement and peace of mind for the people of the world through JVC brand video camera, projectors, headphones, audio, car audio products and professional business products.
www.us.jvc.com
Unfortunately they do not state what "maximum power" refers to, peak or sustained/rms.
I SUSPECT the full bandwidth power rating is RMS but i don't know.
If you want to use full range/bandwidth speakers (bass, mid, high all in 1 chassis) with more than 22W RMS each you need to purchase an external amplifier aswell.
What i would do is buying nice JBL speakers as pictured above and an external amplifier.
Edit:
JVC also does not state an ohm rating for the "Full Bandwith Power" figure.
Normally it would be something like 22W x 4 @ 4 Ohm. But there is no ohm rating. I would use an external amplifier.