A quasi-orthogonal (QO) set of sequences is a union of a number of different orthogonal sets of sequences, where all the sequences are of the same length and energy, such that the absolute value of the inner product of any two sequences belonging to the different orthogonal sets is much less than the energy of the sequences. In this paper we present several supersets of QO sequences, each being a union of an existing QO set and a number of new QO sets obtained through the unique transformations of the existing QO set. Three interesting specific QO supersets are considered, based on the QO sets of quadratic polynomial phase sequences transformed through the signature sequences such as: the higher-degree polynomial phase sequences, the Constant Amplitude Zero Autocorrelation (CAZAC) sequences (in particular, the Bjorck sequences), and m-sequences.