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We study 3d theories containing $\mathcal{N}=3$ Chern-Simons vectormultiplets coupled to the $\mathrm{SU}(N)^3$ flavour symmetry of 3d $T_N$theories with Chern-Simons level $k_1$, $k_2$ and $k_3$. It was formerlypointed out that these theories flow to infrared SCFTs with enhanced$\mathcal{N}=4$ supersymmetry when $1/k_1+1/k_2+1/k_3=0$. We examinesuperconformal indices of these theories which reveal that supersymmetry of theinfrared SCFTs may get enhanced to $4 \leq \mathcal{N} \leq 6$ if such acondition is satisfied. Moreover, even if the Chern-Simons levels do not obeythe aforementioned condition, we find that there is still an infinite family oftheories that flows to infrared SCFTs with $\mathcal{N}=4$ supersymmetry. The't Hooft anomalies of the one-form symmetries of these theories are analysed.As a by-product, we observe that there is generally a decoupled topologicalsector in the infrared. When the infrared SCFTs have $\mathcal{N} \geq 4$supersymmetry, we also study the Higgs and Coulomb branch limits of the indiceswhich provide geometric information of the moduli space of the theories inquestion in terms of the Hilbert series.

Chern-Simons-Trinion Theories: One-form Symmetries and Superconformal Indices