How did you achieve your results 2 and 3? If you know how to do it, why are you asking? Did you use some other tool? Was that other tool using HSL or HSB colorspace. That is important to get the right colors. What do the numbers H: 75, S: 55, L: -25 mean? That is in what range are they. Are they additive or multiplicative? It is important to know what your other tool was doing in order to figure out how to utilize IM and if modulate can even be used.
Looks to me like your other tool may be adding to H,S,L and not multiplying as -modulate does.
Please note that -modulate will not be able to change saturation on anything that is black/white/gray as it is 0 to start with. Thus a multiplier (expressed as a percent) will still be 0. And modulate won't change the hue of black/white/gray as it has no unique hue. All you can do is change the lightness of the gray/white/black pixels with -modulate.
So far the best I can tell is that your software is doing more of an add than a multiply as in -modulate. It is also treating shades of gray/black/white in some special way, which appears to be perhaps some complement of what I get from the following. Furthermore, your background is gray and so thresholding is not distinguishing the white/black/gray in the image from the hidden gray under the transparency. I also had to fudge your numbers a little. I will try to work on it some more as I have time.
Here is what I have done. Basically convert to HSL space and add some percent to each of the H,S,L channels. I had to extract the alpha channel and add it back again. In the second one, I tried to threshold the S channel to get another mask to composite with the original alpha channel to preserve the gray/white/black.
convert checkboxRadioButtonStates.png \
\( -clone 0 -colorspace HSL -separate \) \
\( -clone 1 -evaluate add 17% \) \
\( -clone 2 -evaluate add 45% \) \
\( -clone 3 -evaluate add -25% \) \
\( -clone 4 -clone 5 -clone 6 -set colorspace HSL -combine -colorspace RGB \) \
\( -clone 0 -alpha extract \) \
-delete 0-6 -alpha off -compose copy_opacity -composite \
checkboxRadioButtonStates3.png
convert checkboxRadioButtonStates.png \
\( -clone 0 -colorspace HSL -separate \) \
\( -clone 1 -evaluate add 17% \) \
\( -clone 2 -evaluate add 45% \) \
\( -clone 3 -evaluate add -25% \) \
\( -clone 4 -clone 5 -clone 6 -set colorspace HSL -combine -colorspace RGB \) \
\( -clone 0 -alpha extract \) \
\( -clone 2 -threshold 0 \) \
\( -clone 8 -clone 9 -compose multiply -composite \) \
-delete 1-6,8,9 -alpha off -compose over -composite \
checkboxRadioButtonStates4.png