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Let T be a measure-preserving Zℓ-action on the probability space (X,B,μ), let q1,…,qm:R→Rℓ be vector polynomials, and let f0,…,fm∈L∞(X). For any ϵ>0 and multicorrelation sequences of the form α(n)=∫Xf0⋅T⌊q1(n)⌋f1⋯T⌊qm(n)⌋fmdμ we show that there exists a nil- sequence ψ for which limN−M→∞1N−M∑n=MN−1|α(n)−ψ(n)|≤ϵ and limN→∞1π(N)∑p∈P∩[1,N]|α(p)−ψ(p)|≤ϵ. This result simultaneously generalizes previous results of Frantzikinakis and the authors.