Given any l-tuple (s1, s2,..., sl) of positive integers, there is an integer N = N (s1, s2,..., sl) such that an orthogonal design of order 2n (s1+s2+...+sl) and type (2ns1, 2ns2,..., 2nsl) exists, for each n ≥ N. This complements a result of Eades et al. which in turn implies that if the positive integers s1, s2,..., s_l are all highly divisible by 2, then there is a full orthogonal design of type (s1, s2,..., sl).