  We construct several towers of scalar quantum field theories with an $O(N)$
symmetry which have higher derivative kinetic terms. The Lagrangians in each
tower are connected by lying in the same universality class at the
$d$-dimensional Wilson-Fisher fixed point. Moreover the universal theory is
studied using the large $N$ expansion and we determine $d$-dimensional critical
exponents to $O(1/N^2)$. We show that these new universality classes emerge
naturally as solutions to the linear relation of the dimensions of the fields
deduced from the underlying force-matter interaction of the universal critical
theory. To substantiate the equivalence of the Lagrangians in each tower we
renormalize each to several loop orders and show that the renormalization group
functions are consistent with the large $N$ critical exponents. While we focus
on the first two new towers of theories and renormalize the respective
Lagrangians to $16$ and $18$ dimensions there are an infinite number of such
towers. We also briefly discuss the conformal windows and the extension of the
ideas to theories with spin-$\frac{1}{2}$ and spin-$1$ fields as well as the
idea of lower dimension completeness.
