Is it permissible to combine the intention of the obligatory ghusl with the intention of a recommended ghusl (such as ghusl for cleanliness) at one time?

If the intention to remove major ritual impurity (janabah) is present, the person performing ghusl (ritual bath) may also intend other ghusls with it, such as for cleanliness or cooling, provided that the intention for worship by removing the impurity or making permissible what was forbidden is achieved. What comes after that is subservient to it. However, if the intention is not to remove ritual impurity, then the ghusl will not remove it.