Overprinting black is something that is typically done in vector based programs as part of the trapping process, such as when printing outlines or text over an image. These items are treated as individual objects and maintain there own color integrity. In Photoshop, even though we are creating the "object" architecture using layers we tend to remove those layers before the printing stage when we save the PSD file as a TIFF or other format. At this point, the topmost layers will retain their unique colors if the blending mode is normal. You are correct that setting a black layer to a blending mode of multiply will cause it to blend with the colors underneath it. However, if you have a high contrast image underneath, then there can be some noticable variation. But Photoshop is one step ahead of you. When you chose black, you are not choosing 0 0 0 100 for your CMYK colors. Photoshop is already using a rich black with TAC taken into account and has the CMYK values of 75 68 67 90 by default. So unless you intentionally change the black color to 0 0 0 100 you will not have any issues with needing to overprint black. It's effectively done for you already!

may be can we do it by changing layer blending to multiply?