Layers in multiplayer changes color back to normal when I try to combine with another layer

If you'd like to post a screenshot that includes your layers, that might help.

Instead of merging layers, try selecting both layers and converting them to a Smart Object (right-click to the right of the name in the Layers panel and select Convert to Smart Object or go to Layer > Smart Objects > Convert to Smart Object). When they are in a Smart Object, the layers are preserved within the Smart Object, so their respective blend modes are maintained within that Smart Object. Depending on your image, however, the blend modes may not interact the same with the content that was below it.