Broadening LED spectrum possible?
Run it at the highest current possible.  It will get hot, and radiate IR just from the heat (like any hot object.)  If you over do it, you will end up with a DED (dark emitting diode.)

Other than that, LED spectrums are pretty much set in stone.  

The wavelength is determined by the materials the LED is made of.  The wavelength will vary a (tiny) bit with temperature, but that's about it.