We search for B0 meson decays into two-body combinations of K0, η, η′, and ϕ mesons in 324×10 6 B¯¯¯B pairs collected with the BABAR detector at the PEP-II asymmetric-energy e+e− collider at SLAC. We measure the following branching fractions (upper limits at 90% confidence level) in units of 10−6 B(B0→ηK0)=1.8+0.7−0.6±0.1(<2.9), B(B0→ηη)=1.1+0.5−0.4±0.1(<1.8), B(B0→ηϕ)=0.1±0.2±0.1(<0.6), B(B0→η′ϕ)=0.2+0.4−0.3±0.1(<1.0), and B(B0→η′η′)=1.0+0.8−0.6±0.1(<2.4), where the first error is statistical and the second systematic.