The Moore–Tachikawa conjecture is that each connected complex semisimple group $G$ determines a two-dimensional topological quantum field theory (TQFT) in a category of Hamiltonian symplectic varieties. We view the Moore–Tachikawa conjecture as a first step in systematically assigning new TQFTs to purely Lie-theoretic data. At the same time, one should expect these new TQFTs to bear a close relation to those conjectured by Moore and Tachikawa. Our manuscript aims to integrate these two points of view. In more detail, let $\mathfrak {g}$ be the Lie algebra of $G$. Consider a conjugacy class $\mathcal {C}$ of parabolic subalgebras of $\mathfrak {g}$. This class determines partial Grothendieck–Springer resolutions $\mu _{\mathcal {C}}:\mathfrak {g}_{\mathcal {C}}\longrightarrow \mathfrak {g}^*=\mathfrak {g}$ and $\nu _{\mathcal {C}}:G_{\mathcal {C}}\longrightarrow G$. We construct a canonical symplectic groupoid $(T^*G)_{\mathcal {C}}\;\substack {\longrightarrow \\[-9pt] \longrightarrow }\;\mathfrak {g}_{\mathcal {C}}$ and quasi-symplectic groupoid $\mathrm {D}(G)_{\mathcal {C}}\;\substack {\longrightarrow \\[-9pt] \longrightarrow }\; G_{\mathcal {C}}$. By considering a Kostant slice $\mathrm {Kos}\subseteq \mathfrak {g}$ and Steinberg slice $\mathrm {Ste}\subseteq G$, we prove that the pairs $(((T^*G)_{\mathcal {C}})_{\text {reg}}\;\substack {\longrightarrow \\[-9pt] \longrightarrow }\;(\mathfrak {g}_{\mathcal {C}})_{\text {reg}},\mu _{\mathcal {C}}^{-1}(\mathrm {Kos}))$ and $((\mathrm {D}(G)_{\mathcal {C}})_{\text {reg}}\;\substack {\longrightarrow \\[-9pt] \longrightarrow }\;(G_{\mathcal {C}})_{\text {reg}},\nu _{\mathcal {C}}^{-1}(\mathrm {Ste}))$ determine new and explicit TQFTs in a $1$-shifted Weinstein symplectic category. We then show that certain symplectic varieties arising from our new TQFTs have canonical Lagrangian relations to the open Moore–Tachikawa varieties.