You're mostly better off doing that in software, for two main reasons. One has been mentioned - we have to use quite different detector technologies and optical layouts to get any useful efficiency in different parts of the spectrum. And even in cases where you can use, say, CCD chips treated for reasonable efficiency in the near-UV, the scattering of more intense visible light in many diffraction gratings means that you're better off using a different detector which is "solar blind" - i.e. does not respond at all to long-wavelength radiation. Similarly, detectors that work well in the IR tend to lose their sensitivity much shortward of one micrometer.

A second factor is that for any but the brightest objects, exposure times for decent spectral signal-to-noise ratio are so long that the results aren't seen in real time anyway. There do exist a large number of targets for which one could, for example, load up archival spectra through the UV, optical spectra from the Sloan Digital Sy Survey, and IR spectra from ISO, IRAS, or Spitzer, and browse the results. One of the IRAS team did some interesting work (almost 25 years ago now!) on automated classification of their IR spectra - are there natural classes to those which we didn't know to look at or target for? One obvious advantage to such multiwavelength astrophysics is that the spectral features which are relevant to a particular physical process will not necessarily fall close together in wavelength.