"variously defined" is correct and usable in written English.
You can use it to describe a concept or term that has many different definitions or interpretations. For example: The concept of success is variously defined, depending on a person's individual goals and values.
Antiques have been variously defined by law for tariff purposes.
Calorie, a unit of energy or heat variously defined.
The term confession has been variously defined in the context of contemporary criminal justice.
Canaan, area variously defined in historical and biblical literature, but always centred on Palestine.
This group can be variously defined as stretching from the top 0.003% of the population (the richest thousand persons) to the top 10%.
Instead, present medical classifications offer up a smorgasbord of disorders variously defined by the quality of nervousness, the object of terror, or its source.
Placelessness — variously defined, at varying levels of privilege — might even be seen as becoming the center of gravity of the human condition.
(A Romneyism can be variously defined as an awkward or clueless phrase, a cryptic new policy made up on the fly, or an unaccountable revision of history).
By an odd convergence, both the minimalists and the black nationalists of the 1960's sought to liberate music from shapely melody, which they variously defined as exhausted, oppressive and Eurocentric.
Food insecurity is variously defined as experiencing hunger, inability to secure enough food of sufficient quality and quantity to enable good health and participation in society, and cutting down on food due to financial necessity.
The celebrated 'Lubitsch Touch' has been variously defined, but the touch is of a master chef who knows exactly the right amount of spice or sugar to add to a dish.
