Let π \pi be a ∗ * -representation of a ∗ * -algebra A \mathfrak {A} . In general the strong commutant π ( A ) ′ s \pi {\left ( \mathfrak {A} \right )’ }_s and Theory weak commutant π ( A ) w \pi {\left ( \mathfrak {A} \right ) }_w of the O ∗ {\mathcal {O}^*} -algebra π ( A ) \pi \left ( \mathfrak {A} \right ) do not coincide. We are looking for some methods to get extensions of π \pi such that the related commutants coincide or which are even selfadjoint. In §§2 and 3 we consider so-called generated extensions that are a modification of induced extensions investigated by Borchers, Yngvason [1] and Schmüdgen [7]. In §4 let A \mathfrak {A} be a ∗ * -algebra and B \mathfrak {B} a subset of its hermitian part A h {\mathfrak {A}_h} such that A \mathfrak {A} is generated by B ∪ { 1 } \mathfrak {B} \cup \left \{ 1 \right \} as an algebra. We present a method to extend ∗ * -representations π \pi of such algebras, which is closely related with the extension of the symmetric operators π ( b ) , b ∈ B \pi \left ( b \right ),b \in \mathfrak {B} . In §5 we give an example that shows that the method of generated extensions is also suitable to get extensions such that the commutants of the related O ∗ {\mathcal {O}^*} -algebras coincide.