Renormalization group theory does not restrict the form 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., β, γ, ν) vary keeping others (e.g., δ, η) fixed. Here we report ferromagnetic phase transition in (Sm1-yNdy)0.52Sr0.48MnO3 (0.5 ≤ y ≤ 1) single crystals where all three exponents β, γ, δ vary with Nd concentration y. Such a 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 multi-criticality.