We study the existence of various sign and value patterns in sequences defined by multiplicative functions or related objects. For any set
$A$
whose indicator function is ‘approximately multiplicative’ and uniformly distributed on short intervals in a suitable sense, we show that the density of the pattern
$n+1\in A$
,
$n+2\in A$
,
$n+3\in A$
is positive as long as
$A$
has density greater than
$\frac{1}{3}$
. Using an inverse theorem for sumsets and some tools from ergodic theory, we also provide a theorem that deals with the critical case of
$A$
having density exactly
$\frac{1}{3}$
, below which one would need nontrivial information on the local distribution of
$A$
in Bohr sets to proceed. We apply our results first to answer in a stronger form a question of Erdős and Pomerance on the relative orderings of the largest prime factors
$P^{+}(n)$
,
$P^{+}(n+1),P^{+}(n+2)$
of three consecutive integers. Second, we show that the tuple
$(\unicode[STIX]{x1D714}(n+1),\unicode[STIX]{x1D714}(n+2),\unicode[STIX]{x1D714}(n+3))~(\text{mod}~3)$
takes all the
$27$
possible patterns in
$(\mathbb{Z}/3\mathbb{Z})^{3}$
with positive lower density, with
$\unicode[STIX]{x1D714}(n)$
being the number of distinct prime divisors. We also prove a theorem concerning longer patterns
$n+i\in A_{i}$
,
$i=1,\ldots ,k$
in approximately multiplicative sets
$A_{i}$
having large enough densities, generalizing some results of Hildebrand on his ‘stable sets conjecture’. Finally, we consider the sign patterns of the Liouville function
$\unicode[STIX]{x1D706}$
and show that there are at least
$24$
patterns of length
$5$
that occur with positive upper density. In all the proofs, we make extensive use of recent ideas concerning correlations of multiplicative functions.