On the other hand, it is almost always possible to mix the "bright" inks to produce any color producable by the "dull" inks, that is essentially what is happening with colorants on your computer monitor right now, as you view the above illustration. The full range of colors that can be produced by any color reproduction system is called the color "gamut" of that system.
Curiously, this very real phenomenon is made a scapegoat for all kinds of other deficiencies in color management, for instance we've actually heard it blamed for an inability to match SWOP printing values with the "extreme" gamut inks sold by some large-format inkjet manufacturers. Nothing could be further from reality. With real color management of the sort discussed elsewhere at this web site, one always wants the most "extreme" gamut available. Simulation of other systems, such as SWOP, is thereafter simple because all of the desired colors are available.
It is popular to draw a picture of available colors (a color "space") as a colored disk, and to then draw out the available gamut as a polygon on that illustration.

In this illustration, the black polygon corresponds to the "bright" inks, and the white polygon, corresponds to the "dull" inks. The colored disk on which the polygons are displayed is typically a "plane" from within a "CIE color space". This is a handy way that color scientist display the relationship between the "gamuts" of two different color reproduction systems. The fact that all the colors acheivable by the "dull" inks are also acheivable by the "bright" inks is nicely illustrated. The fact that the bright inks can acheive colors that can't be acheived by the dull inks is likewise illustrated.
One simple solution is to move all the points outside the white polygon directly inward to the nearest point on that polygon, while matching all other points as accurately as possible. This provides the best possible match to all colors that can be accurately matched, and is great for hitting spot colors, but it tends to produce lousy reproductions of photographs. Consider a photograph of an apple in which the reds of a highlights have to all be moved, and that by these rules they're all moved to the same point on the white polygon. As we view the photograph, we'll see a terrible "fringe" surrounding the highlight as the area of out-of-gamut colors that have been run-together transitions to the area where more accurate color reproduction is possible.
This is often called a "colorimetric" correction, and if you have a "colorimetric ICC profile", this is what you've got.
A more satisfactory solution would be to somehow "deform" the entire surface of the above diagram so that all points are moved into the white polygon, while avoiding "clipping" colors so that colors that differed in the original are knocked down to be the same color in the reproduction. Colors that are within the reach of the dull inks (inside the white polygon) will be less accurately reproduced, but your reproductions will be free of the nasty "fringes" described above.
This is often called a "perceptual" or "photometric" correction and if you have a "perceptual ICC profile", this is what you've got.
There is a infinite variety of ways to perform these "deformations" of the "color space", and this is the real art of color management. The beauty of standards for exchanging these things, such as the ICC profile standard, is that if you don't like one supplier's art, it is easy to substitute another's, or to substitute your own.
If you find that you can't do this, don't go back to dull inks - get better color management. Solving the problem by going back to dull inks is like buying an abacus to replace your computer. There is real color management available, and it's reasonable for you to insist on using it.