Four new equivalence classes of finite loops are considered: $C$-, $R$-, $E$-classes, and parastrophic closures. The first three classes are natural interclasses between isomorphic and isotopy classes of loops. Their internal isotopies are characterized and a way for generating isotopy classes from $C$-classes and $R$-classes is pointed to. The exact upper bound for the length of parastrophic closures is determined.