  We study the phase diagram of the isotropic $J_{1}$--$J_{1}'$--$J_{2}$
Heisenberg model for spin-1 particles on an anisotropic square lattice, using
the coupled cluster method. We find no evidence for an intermediate phase
between the N\'{e}el and stripe states, as compared with all previous results
for the corresponding spin-1/2 case. However, we find a quantum tricritical
point at $J_{1}'/J_{1} \approx0.66 \pm 0.03$, $J_{2}/J_{1} \approx0.35\pm0.02$,
where a line of second-order phase transitions between the quasi-classical
N\'{e}el and stripe-ordered phases (for $J_{1}'/J_{1} \lesssim 0.66$) meets a
line of first-order phase transitions between the same two states (for
$J_{1}'/J_{1} \gtrsim 0.66$)
