SCSS multiclass BEM model @mixin.

input.html

<div class="bg_white-black"></div>

input.scss

@mixin el($name) {
@at-root #{&}[class*="_#{$name}"] {
    @content;
  }
}
@mixin md($name) {
@at-root #{&}[class*="-#{$name}"] {
    @content;
  }
}
$model: bg;
[class*="#{$model}"] {
  border: gray 1px solid;
  @mixin colors() {
    @include md(black){
      color: black;
    }
  }
  @at-root {
    @include el(white) {
      background-color: white;
      @include colors;
    }
    @include el(lightgray) {
      background-color: lightgray;
    }
  }
}

output.css

[class*="bg"] {
  border: gray 1px solid;
}
[class*="bg"][class*="_white"] {
  background-color: white;
}
[class*="bg"][class*="_white"][class*="-black"] {
  color: black;
}
[class*="bg"][class*="_lightgray"] {
  background-color: lightgray;
}