To do this would be unusual in several ways. First, because you only need about a 2X gain in signal voltage to get where you need to be in terms of input sensitivity, whereas most SUTs operating into an MM phono stage are designed and built to yield at least a 10X voltage gain. But more importantly (second), the load resistor in your MC phono stage is most likely lower in value than that of a typical MM phono stage (47K ohms is pretty much standard for MM). Typically an MC phono stage will provide an input resistance of about 1000 ohms and often much less. When you hook up a SUT, you get a reduction of the impedance seen by the cartridge (defined as a resistance that varies with frequency) equal to the square of the turns ratio of the SUT. Thus, if your phono stage has a 1000 ohm resistor at its input, and assuming you are using a SUT that gives you 10X gain (which would really be too much gain, but I don't know where you'll find a SUT with less gain), then the cartridge would have to drive a 10-ohm impedance (1000 divided by 100). This means ideally that your cartridge needs to have an internal resistance of 1 or 2 ohms to be able to drive such a load. Only a very few MCs are that low. If your stage has a 100-ohm fixed resistance (quite possible), you would really be in the soup; that won't work. So, the first thing to do is to determine what is the value of the resistance at the phono input. Second thing to do is to see if you can find a commercially made SUT with a gain factor less than 4 or 5. (Gain is equal to the "turns ratio".) If the input resistance is high enough and if the gain of the SUT is low enough, you might have a fighting chance that your cartridge will drive it.
By the way, have you auditioned what you've got, or are you just going by the given specifications? Because you're not too far away from a combo that might work as is. I'd give it a shot.