I don't have experience with the D610 but if it's similar with the D600, yes it sort of have a multiple exposure mode. It's the same as the "Bracketing" for HDR but just set it to not change EV values on the different exposures. Also, it's limited to 3 exposure - that's it. And also, no, you cannot scoot back and expose over images you already have in your card - it's a feature not a bug - you have enter the big boys world of semi-pro photo equipment - read on!
Now you must understand that with the D610 you have moved into the level of "Pro-Consumer" aka "Professional-Consumer" grade of cameras and all these funky options found in kids cameras or strictly consumer grade cameras will not be easily accessible or even available. If you want to do multiple exposure, in 2014, you do it in post-production - Photoshop, Elements etc where you can control the overlap and the transparent/opaqueness of each frame when they overlap. It's much more accurate, you have much more control of the shooting environment and the compilation of the shots and certainly will have much better results.