A 2-$$(v,k,\lambda )$$
(
v
,
k
,
λ
)
design is additive (or strongly additive) if it is possible to embed it in a suitable abelian group G in such a way that its block set is contained in (or coincides with) the set of all zero-sum k-subsets of its point set. Explicit results on the additivity or strong additivity of symmetric designs and subspace 2-designs are presented. In particular, the strong additivity of PG$$_d(n,q)$$
d
(
n
,
q
)
, which was known to be additive only for $$q=2$$
q
=
2
or $$d=n-1$$
d
=
n
-
1
, is always established.