How can I influence one material on another

There are two materials on the mesh:
The first material is the basic texture of the character
The second material is responsible for alpha and makes the object transparent

The second object should make the first one transparent (now it only makes itself transparent) Can I multiply them somehow or change the blending method like in Photoshop?

What you should do is have a shader with multiple passes rather than two materials, then use blend modes in the different passes to achieve the effect you want. You can read about shader blend modes in the docs here: Unity - Manual: ShaderLab command: Blend