onsider stochastic reaction-diffusion equations driven by multiplicative space-time white noise. When the noise disappears, it is well known that such PDEs with superlinear frequently have non-trivial stationary solutions. By contrast, Bonder and Groisman have recently shown that there is finite-time blowup when there is appearance of noise. In this paper, we prove that the Bonder--Groisman condition is unimproveable. We present two essentially-different ways of approaches without altering the conclusions of our assertions.