  In this paper, we establish three new and general transformations with
sixteen parameters and bases via Abel's lemma on summation by parts. As
applications, we set up a lot of new transformations of basic hypergeometric
series. Among include some new results of Gasper and Rahman's quadratic, cubic,
and quartic transformations. Furthermore, we put forward the so-called
$(R,S)$-type transformation with arbitrary degree to unify such multibasic
transformations. Some special $(R,S)$-type transformations are presented.
