It has long been unclear whether the theory of plethystically modified Macdonald polynomials H_mu(X;q,t) = J_mu[X/(1-t);q,t] could be enriched by lifting it to the nonsymmetric setting. We construct such a lift by defining a nonsymmetric version, Pi_r, of the plethystic transformation f[X] -> f[X/(1-t)]. Applying Pi_r to a stable version of the nonsymmetric Macdonald polynomials yields a new family of modified r-nonsymmetric Macdonald polynomials, H_{eta | lambda}(X;q,t), with positivity properties bearing a striking resemblance to those of the symmetric polynomials H_mu. In particular, the H_{eta | lambda} are monomial positive and are conjecturally positive in the Demazure atom basis. Moreover, H_{eta | lambda} admits a combinatorial expansion as a positive sum of flagged LLT polynomials, a nonsymmetric variant of LLT polynomials.