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We consider a state-space model {Xt, Yt}t≥1 with a static parameter θ governing its transition and observation probability laws. Our work concerns Bayesian inference of θ given Y1:n for some n ≥ 1. When the state-space model is non-linear or non-Gaussian, the inference is utilised with sequential Monte Carlo (SMC). In particular, in the Metropolis-within-particle Gibbs algorithm, an iteration consists of (i) updating the sample for X1:n via a conditional SMC (cSMC), which is followed by (ii) a Metrpolis-Hastings update for θ . Retaining one path from the samples in the cSMC involved in Metropolis-within- particle Gibbs may seem to be wasteful. A natural question is whether it is possible to make use of multiple, even all possible, trajectories and average out the corresponding acceptance ratios. We show that this is possible via the use of asymmetric acceptance ratios. The proposed schemes reduce asymptotic variance at a cost that can be parallellised.