Point one style class to another?

You can use selector grouping:

.foo, .list1 li { 
  background-color: red; 
} 

No. The best you can do with "native CSS" is to use a multiple selector:

.foo, .list1 li {
   ...
}

Otherwise there are preprocessors that can help with this such as SASS.

Not with any syntax like that (and don't confuse a "class" (an HTML term) with a "class selector" or a "rule-set").

Your options are multiple classes, grouping selectors or preprocessing.