  A combination of a finite number of linear independent states forms
superposition in a way that cannot be conceived classically. Here, using the
tools of resource theory of superposition, we give the conditions for a class
of superposition state transformations. These conditions strictly depend on the
scalar products of the basis states and reduce to the well-known majorization
condition for quantum coherence in the limit of orthonormal basis. To further
superposition-free transformations of $d$-dimensional systems, we provide
superposition-free operators for a deterministic transformation of
superposition states. The linear independence of a finite number of basis
states requires a relation between the scalar products of these states. With
this information in hand, we determine the maximal superposition states which
are valid over a certain range of scalar products. Notably, we show that, for
$d\geq3$, scalar products of the pure superposition-free states have a greater
place in seeking maximally resourceful states. Various explicit examples
illustrate our findings.
