  We study a natural growth process with competition, modeled by two first
passage percolation processes, $FPP_1$ and $FPP_\lambda$, spreading on a graph.
$FPP_1$ starts at the origin and spreads at rate $1$, whereas $FPP_\lambda$
starts from a random set of \emph{inactive seeds} distributed as Bernoulli
percolation of parameter $\mu\in (0,1)$. A seed of $FPP_\lambda$ gets activated
when one of the two processes attempts to occupy its location, and from this
moment onwards spreads at some fixed rate $\lambda>0$. In previous works~[17,
3, 7] it has been shown that when both $\mu$ or $\lambda$ are small enough,
then $FPP_1$ \emph{survives} (i.e., it occupies an infinite set of vertices)
with positive probability. It might seem intuitive that decreasing $\mu$ or
$\lambda$ is beneficial to $FPP_1$. However, we prove that, in general, this is
indeed false by constructing a graph for which the probability that $FPP_1$
survives is not a monotone function of $\mu$ or $\lambda$, implying the
existence of multiple phase transitions. This behavior contrasts with other
natural growth processes such as the $2$-type Richardson model.
