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

‎a $mu$-way $(v,k,t)$ $trade$ of volume $m$ consists of $mu$‎ ‎disjoint collections $t_1$‎, ‎$t_2‎, ‎dots t_{mu}$‎, ‎each of $m$‎ ‎blocks‎, ‎such that for every $t$-subset of $v$-set $v$ the number of‎ ‎blocks containing this t-subset is the same in each $t_i (1leq‎ ‎i leq mu)$‎. ‎in other words any pair of collections ${t_i,t_j}$‎, ‎$1leq i< j leq mu‎$ is a $(v,k,t)$ trade of volume $m$. in this paper we investigate the existence of $mu$-way $(v,k,t)$ trades and prove‎ ‎the existence of‎: ‎(i)~3-way $(v,k,1)$ trades (steiner‎ ‎trades) of each volume $m,mgeq2$‎. ‎(ii) 3-way $(v,k,2)$ trades of‎ ‎each volume $m,mgeq6$ except possibly $m=7$‎. ‎we establish the‎ ‎non-existence of 3-way $(v,3,2)$ trade of volume 7‎. ‎it is shown that‎ ‎the volume of a 3-way $(v,k,2)$ steiner trade is at least $2k$ for‎ ‎$kgeq4$‎. ‎also the spectrum of 3-way $(v,k,2)$ steiner trades for‎ ‎$k=3$ and 4 are specified‎.