Can you search for base64 with grep?

Is it possible to search for Base64 strings with grep? Say I have a list of text files and I want to find all the Base64 strings contained in them; is there any way to search for them? I mean I know they usually end with = or == and they also have sequences of bytes which relate to what letters they are encoded as within the base64 string. But as for searching for them in general (without knowing anything about what is encoded) I don't really know how to do so.