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We use 5-brane webs to study the two-dimensional space of supersymmetric massdeformations of higher rank generalizations of the 5d $E_1$ and $\tilde{E}_1$theories. Some of the resulting IR phases are described by IR freesupersymmetric gauge theories, while others correspond to interacting fixedpoints. The number of different phases appears to grow with the rank. The spaceof deformations is qualitatively different for the even and odd rank cases, butthat of the even (odd) rank $E_1$ theory is similar to that of the odd (even)rank $\tilde{E}_1$ theory. One result of our analysis predicts that thesupersymmetric $SU(N)$ theory with CS level $k=\frac{N}{2} + 4$ and a singlemassless antisymmetric hypermultiplet exhibits an enhanced global symmetry atthe UV fixed point, given by $SU(2)\times SU(2)$ if $N$ is even, and$SU(2)\times U(1)$ if $N$ is odd.

The Cat's Cradle: Deforming the higher rank $E_1$ and $\tilde{E}_1$ theories