Let's change the direction of our investigations: rather than consider smaller varieties let us consider the larger varieties of all nil-k groups.

   It isn't hard to construct examples similar to the ones in nil-2 groups to quickly establish that in these varieties there are nontrivial dominions. An exact description of the dominions, however, is still lacking (as are necessary and sufficient conditions for embeddability, weak and strong, of amalgams).

   But say that I start with a nil-2 group G, a subgroup H, and its dominion D in the variety of all nil-2 groups; and then, I shift my category of context to that of all nil-k groups. Since there are more groups and hence more morphisms here, it is possible that the dominion of H will shrink when changing the context.

   As it turns out, dominions of nil-2 groups can be very resilient (up to a point). There exists a finitely generated nil-2 group G such that for any k>0, there is a subgroup H (which depends on k) such that the dominion of H in G in N2 is nontrivial, and is equal to the dominion in the variety of all nil-k groups. There also exists an infinitely generated group G and a finitely generated subgroup H of G which is properly contained in its dominion, and the dominion remains stable when changing the context to the category of all nilpotent groups of any class (which is not a variety, only a pseudovariety).

   The limits of this is that the dominion of a subgroup of a finitely generated nilpotent group (of any class) is trivial in the category of all nilpotent groups. Also, the dominion of a subgroup of a finitely generated nil-2 group is trivial in the category of all metabelian nilpotent groups. (A group is metabelian if it is solvable of length at most two). These results can be found in Dominions in finitely generated nilpotent groups, Arturo Magidin, Comm. Algebra 27 no. 9 (1999), 4545-4559.