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The present paper is related to some recent studies in Abdollahi and Russo [‘On a problem of P. Hall for Engel words’, Arch. Math. (Basel) 97 (2011), 407–412] and Fernández-Alcober et al. [‘A note on conciseness of Engel words’, Comm. Algebra 40 (2012), 2570–2576] on the position of the 
$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}n$-Engel marginal subgroup 
$E^*_n(G)$ of a group 
$G$, when 
$n=3,4$. Describing the size of 
$E^*_n(G)$ for 
$n=3,4$, we show some generalisations of classical results on the partial margins of 
$E^*_3(G)$ and 
$E^*_4(G)$.
