It may, if you use a memory foam bed topper which is firm. A number of people use their memory foam toppers to “repair” their sagging mattresses. Although this is not a usage that is recommended by the manufacturer, it is done, and from the feedback received, it works. Obviously, a sagging mattress is not quite the same as a mattress that is too soft, but the principles are the same.
Having said that, firmness you receive from doing this may not be too steady. By putting a firm memory foam mattress topper on top of a soft mattress, you are basically reversing things – the base has become the top, and all that … There is a good reason why people usually put a firm mattress below and a soft topper on top.
The biggest problem with this role reversal between mattress and topper is that the topper will deteriorate faster than usual. Even if you got a good deal from a memory foam topper discount sale, it is a bit of a waste.
If your mattress is too soft, you may actually find it more effective to ditch the mattress and buy a memory foam mattress pad of the right firmness or hardness for your body. Since you prefer something firm, one of the thinner 2.5-inch memory foam mattress pads should be good enough. Everything else being equal, this is one of the most economical thicknesses you can buy.