We would first like to thank the reviewers for their erudite and helpful reviews. All reviewers clearly took the time to fully understand the work and provide constructive feedback. We will look to address the concerns raised in the revised version of the paper; in particular we will revise in Section 3 to provide a more detailed description of iPMCMC and the motivation behind it. We will also clarify the specific ambiguities that have been raised. $ Assigned_Reviewer_1: Although comparisons to serialized PMCMC variants are provided in the supplementary material, we acknowledge that these could have been summarized more clearly in the main paper. A key point is that it is possible to run iPMCMC in a serial fashion, which only requires O(N+M) memory (retaining a single sampled trajectory and the marginal likelihood estimate from each sweep), compared to O(NM) for running M times more particles. For the tested models, iPMCMC significantly outperforms a single PG run for M times more iterations (see Figures 4, 5c and 5d). Therefore, although running more particles when using a single core will generally be preferable, iPMCMC still offers significant advantages even without parallelization when memory is limited. Ancestor / backward sampling can be applied in the iPMCMC case in the same way as the standard PG case. However, whereas iPMCMC equally applies to non-Markovian models and requires only forward simulation, ancestor sampling is not always practical or even possible in some scenarios. The comment about the conditional node indices being distinct is simply stating that the same worker cannot be sampled more than once in lines 5-8 of Algorithm 3 such that at each iteration r, all the retained particles are different. We will make sure to extend section 3.3 to include a more detailed and clear discussion of how the switching probability depends on sigma, M, P and N. Assigned_Reviewer_2: We do indeed generate the initial trajectories using P SMCs. We agree that the increased degeneracy issues of PG at the earlier states is the source of the superior performance of iPMCMC in this region. The point that iPMCMC gives similar (or possibly worse) performance for the LGSSM than the alternatives whilst all methods are in the burn in period is intriguing and may be associated with the fact that iPMCMC, unlike the non-interacting methods, does not have even weighting for the different nodes. In general we expect this to be beneficial but it may be the case that it is not for very small sample sizes. The suggested theoretical extensions and parallels in the literature are interesting and much appreciated! Assigned_Reviewer_3: We realise that our explanation of the relationship between iPMCMC and i-c-alphaSMC introduced by Huggins & Roy (2015) was slightly ambiguous. To clarify, although iPMCMC falls within this i-c-alphaSMC framework when (and only when) P=1, it corresponds to a very particular instance of i-c-alphaSMC which has not been previously suggested. Deriving this equivalent instance would require, amongst other things, the design of an appropriate scheme for setting alpha that avoids the need for all samples to be communicated to a single node when sampling the retained particle. Additionally, while the extension from P=1 to P>1 might seem conceptually simple at a high level, the theoretical justification for iPMCMC with P>1 in fact requires us to use a different extended target construction than what is used in i-c-alphaSMC or standard PMCMC. Figure 1 furthermore demonstrates the significant empirical advantages that using P > 1 brings. We acknowledge that the presented experimental benchmarks do not include a case in which no existing methods would give a satisfactory performance in reasonable time. Our intention was to illustrate iPMCMC in very simple settings to obtain easily interpretable results and we are confident that the results obtained in these simple scenarios will carry over to more complicated settings (where existing methods will be insufficient). However, we do agree that it would be even better to illustrate this explicitly on such an example and will thus try to add a more challenging experiment in time for the revised version. We will make sure to clarify practical issues of distribution in a revised version. At each iteration only a single particle trajectory and weight need be communicated between the nodes and the time taken for calculation of the updates of the CSMC node ids is negligible. We do hope to extend to an asynchronous implementation in future work.