If I understand properly, QM says a particle can only be entangled with one other particle. How then can you get entangled ensembles of particles, required for example in various theories of decoherence or in notions of fast scrambling in black holes or in tensor networks? I'm sure I'm missing something, and those examples are not necessarily related, but it seems they all require distributed entanglement in some form or other.
QM says a particle can only be entangled with one other particle
This is not correct.
These are the postulates of quantum mechanics, chosen to fit the data as far as observations and measurements of the present day.
Of these the wavefunction postulate is crucial for the definition of ".entanglement"
It is one of the postulates of quantum mechanics that for a physical system consisting of a particle there is an associated wavefunction .
For two bodies there exist solutions of Schrodinger or Dirac or Klein Gordon equations with a wavefunction.
The quantum mechanical many body problem is approached with quantum field theory, a theoretical level and calculational method above the simple solution of QM equations, but based on the postulates , including the wavefunction, of basic quantum mechanics. One gets an approximation to a collective wavefunction, for the system under study, and the particles there are "entangled" in principle, by the interactions, energy and momentum conservation and all the quantum numbers involved
Or for a large number of atoms in principle there exist quantum mechanical models that approximate the wavefunction of large systems of particles , as for example in the band theory of solids.