  We study the problem of fairly allocating indivisible goods between groups of
agents using the recently introduced relaxations of envy-freeness. We consider
the existence of fair allocations under different assumptions on the valuations
of the agents. In particular, our results cover cases of arbitrary monotonic,
responsive, and additive valuations, while for the case of binary valuations we
fully characterize the cardinalities of two groups of agents for which a fair
allocation can be guaranteed with respect to both envy-freeness up to one good
(EF1) and envy-freeness up to any good (EFX). Moreover, we introduce a new
model where the agents are not partitioned into groups in advance, but instead
the partition can be chosen in conjunction with the allocation of the goods. In
this model, we show that for agents with arbitrary monotonic valuations, there
is always a partition of the agents into two groups of any given sizes along
with an EF1 allocation of the goods. We also provide an extension of this
result to any number of groups.
