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A $\mu$-way $(v,k,t)$ $trade$ of volume $m$ consists of $\mu$ disjointcollections $T_1$, $T_2, \dots T_{\mu}$, each of $m$ blocks, such that forevery $t$-subset of $v$-set $V$ the number of blocks containing this t-subsetis the same in each $T_i\ (1\leq i\leq \mu)$. In other words any pair ofcollections $\{T_i,T_j\}$, $1\leq i<j \leq \mu$ is a $(v,k,t)$ trade of volume$m$.  In this paper we investigate the existence of $\mu$-way $(v,k,t)$ trades andalso we prove the existence of: (i)~3-way $(v,k,1)$ trades (Steiner trades) ofeach volume $m,m\geq2$. (ii) 3-way $(v,k,2)$ trades of each volume $m,m\geq6$except possibly $m=7$. We establish the non-existence of 3-way $(v,3,2)$ tradeof volume 7. It is shown that the volume of a 3-way $(v,k,2)$ Steiner trade isat least $2k$ for $k\geq4$. Also the spectrum of 3-way $(v,k,2)$ Steiner tradesfor $k=3$ and 4 are specified.

On the possible volume of $\mu$-$(v,k,t)$ trades