Unable To Increase Saturation With Untagged CMYK File

Digitaldog is right, "Don't Color Manage" IS bad.

AND there's no such thing as viewing in Photoshop without colour management, when you open an untagged file the default ICC profile from color settings u is used - in this case the default CMYK - if you're seeing significantly unexpected colour on just one image then that image was probably separated differently. 

Providing untagged CMYK as a last stage of delivery is OK BUT the CMYK image files must have been generated correctly from the RGB originals.

The recipient (printer?) should really tell you

"separate to XXXCMYK.icc and, when saving a copy to send to us, remove the ICC profile. (i.e. save untagged)"

The separation (conversion) of RGB to CMYK sets the vital ink recipes, the colour accuracy depends on those ink recipes - if the wrong CMYK profile is used then the ink recipes differ and the printed result could be very poor.

SO, as I wrote its OK to strip the profile (but that does remove the ability of a subsequent viewer to look at the image digitally with confidence that they see what you saw) - BUT the CMYK file MUST have been made using the right CMYK profile.

There's no "generic" CMYK, a CMYK ICC profile is a set of instructions to hit a target. Wrong instructions, target missed!

I hope this helps
neil barstow, colourmanagement net - adobe forum volunteer - co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

Can you fiddle with the saturation on the RGB? Is the printer wanting an RGB file? If so they are using a copier not a press to print. Copiers tend to make images more saturated. Will you get a proof?

First: Don't Color Manage is bad! 

Next, the color gamut of many CMYK color spaces is much smaller than many RGB color spaces. You can't up saturation that can't exist! What was the color space of the RGB original? 

Think the color gamut of most RGB color spaces as having a range from 0 to 10 and CMYK as 0 to 8; you can't go any higher than 8. You converted from RGB to CMYK and that's the limit. 

And then there's the huge disconnect between the shape of the gamut and size of the gamut of your display, and CMYK. 

Even with RGB alone, depending on the output device, some Working Space gamuts are better than others for output:

The benefits of wide gamut working spaces on printed output:

This three-part, 32-minute video covers why a wide gamut RGB working space like ProPhoto RGB can produce superior quality output to print.

Part 1 discusses how the supplied Gamut Test File was created and shows two prints output to an Epson 3880 using ProPhoto RGB and sRGB, how the deficiencies of sRGB gamut affect final output quality. Part 1 discusses what to look for on your own prints in terms of better color output. It also covers Photoshop’s Assign Profile command and how wide gamut spaces mishandled produce dull or oversaturated colors due to user error.

Part 2 goes into detail about how to print two versions of the properly converted Gamut Test File file in Photoshop using Photoshop’s Print command to correctly setup the test files for output. It covers the Convert to Profile command for preparing test files for output to a lab.

Part 3 goes into color theory and illustrates why a wide gamut space produces not only move vibrant and saturated color but detail and color separation compared to a small gamut working space like sRGB. 

High Resolution Video: http://digitaldog.net/files/WideGamutPrintVideo.mov
Low Resolution (YouTube): https://www.youtube.com/watch?v=vLlr7wpAZKs&feature=youtu.be