  The pair contact process with diffusion (PCPD) with modulo 2 conservation
(\pcpdt) [$2A\to 4A$, $2A\to 0$] is studied in one dimension, focused on the
crossover to other well established universality classes: the directed Ising
(DI) and the directed percolation (DP). First, we show that the \pcpdt shares
the critical behaviors with the PCPD, both with and without directional bias.
Second, the crossover from the \pcpdt to the DI is studied by including a
parity-conserving single-particle process ($A \to 3A$). We find the crossover
exponent $1/\phi_1 = 0.57(3)$, which is argued to be identical to that of the
PCPD-to-DP crossover by adding $A \to 2A$. This suggests that the PCPD
universality class has a well defined fixed point distinct from the DP. Third,
we study the crossover from a hybrid-type reaction-diffusion process belonging
to the DP [$3A\to 5A$, $2A\to 0$] to the DI by adding $A \to 3A$. We find
$1/\phi_2 = 0.73(4)$ for the DP-to-DI crossover. The inequality of $\phi_1$ and
$\phi_2$ further supports the non-DP nature of the PCPD scaling. Finally, we
introduce a symmetry-breaking field in the dual spin language to study the
crossover from the \pcpdt to the DP. We find $1/\phi_3 = 1.23(10)$, which is
associated with a new independent route from the PCPD to the DP.
