  We consider the edge-reinforced random walk with multiple (but finitely many)
walkers which influence the edge weights together. The walker which moves at a
given time step is chosen uniformly at random, or according to a fixed order.
First, we consider 2 walkers with linear reinforcement on a line graph
comprising three nodes. We show that the edge weights evolve similarly to the
setting with a single walker which corresponds to a P\'olya urn. In particular,
the left edge weight proportion is a martingale at certain stopping times,
showing that a (random) limiting proportion exists. We then look at an
arbitrary number of walkers on Z with very general reinforcement. We show that
in this case, the behaviour is also the same as for a single walker: either all
walkers are recurrent or all walkers have finite range. In the particular case
of reinforcements of "sequence type", we give a criterion for recurrence.
