  Renormalization group theory does not restrict the from of continuous
variation of critical exponents which occurs in presence of a marginal
operator. However, the continuous variation of critical exponents, observed in
different contexts, usually follows a weak universality scenario where some of
the exponents (e.g., $\beta, \gamma, \nu$) vary keeping others (e.g., $\delta ,
\eta$) fixed. Here we report a ferromagnetic phase transition in
(Sm$_{1-y}$Nd$_{y}$)$_{0.52}$Sr$_{0.48}$MnO$_3$ $(0.5\le y\le1)$ single crystal
where all critical exponents vary with $y.$ Such variation clearly violates
both universality and weak universality hypothesis. We propose a new scaling
theory that explains the present experimental results, reduces to the weak
universality as a special case, and provides a generic route leading to
continuous variation of critical exponents and multicriticality.
