$\eta$-pairing symmetry provides exact singlet-pair eigenstates of the Hubbard model but is broken by interlayer density interactions. Here we construct an interlayer spin-triplet pair operator in a spinful multilayer extended Hubbard model. A restricted spectrum-generating algebra yields a tower of exact eigenstates exhibiting off-diagonal long-range order. The double commutator shows that this tower exists for bilayer and trilayer systems with finite interlayer interaction, but the construction fails for four or more layers. We also examine the spin-one structure, the trilayer case, and the relation to on-site singlet $\eta$ pairs. Exact diagonalization locates the tower within the many-body spectrum and gives its entanglement entropy. A calculation on stacked T-shaped clusters finds constant fidelity for three layers and a decrease from unity for four layers.

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• Superfluidity
• Fermionic condensates
• Multilayer & multiplex networks
• Quantum many-body systems
• Strongly correlated systems
• Unconventional superconductors
• Exact solutions for many-body systems
• Hubbard model