A 3-way (v, k, t) trade T of volume m consists of three pairwise disjoint collections T 1 , T 2 and T 3 , each of m blocks of size k, such that for every t-subset of v-set V , the number of blocks containing this t-subset is the same in each T i for 1 ≤ i ≤ 3. If any t-subset of found(T ) occurs at most once in each T i for 1 ≤ i ≤ 3, then T is called 3-way (v, k, t) Steiner trade. We attempt to complete the spectrum S 3s (v, k), the set of all possible volume sizes, for 3-way (v, k, 2) Steiner trades, by applying some block designs, such as BIBDs, RBs, GDDs, RGDDs, and r × s packing grid blocks. Previously, we obtained some results about the existence some 3-way (v, k, 2) Steiner trades. In particular, we proved that there exists a 3-way (v, k, 2) Steiner trade of volume m when 12(k − 1) ≤ m for 15 ≤ k (Rashidi and Soltankhah, 2016). Now, we show that the claim is correct also for k ≤ 14.MSC: 05B30; 05B05