Complex sentence: It is also common to try multiple anti-inflammatories over a further 4--6 week period, if necessary, since an animal will often respond to one type but fail to respond to another.
Split into simpler sentences: It is also common, if necessary, to try multiple anti-inflammatories over a further 4-6 week period. This is since an animal will often respond to one type, but will fail to respond to another.