Active intelligent reflecting surface (IRS) is a revolutionary technique for the future 6G networks. The conventional far-field single-IRS-aided directional modulation(DM) networks have only one (no direct path) or two (existing direct path) degrees of freedom (DoFs). This means that there are only one or two streams transmitted simultaneously from base station to user and will seriously limit its rate gain achieved by IRS. How to create multiple DoFs more than two for DM? In this paper, single large-scale IRS is divided to multiple small IRSs and a novel multi-IRS-aided multi-stream DM network is proposed to achieve a point-to-point multi-stream transmission by creating $K$ ($\geq3$) DoFs, where multiple small IRSs are placed distributively via multiple unmanned aerial vehicles (UAVs). The null-space projection, zero-forcing (ZF) and phase alignment are adopted to design the transmit beamforming vector, receive beamforming vector and phase shift matrix (PSM), respectively, called NSP-ZF-PA. Here, $K$ PSMs and their corresponding beamforming vectors are independently optimized. The weighted minimum mean-square error (WMMSE) algorithm is involved in alternating iteration for the optimization variables by introducing the power constraint on IRS, named WMMSE-PC, where the majorization-minimization (MM) algorithm is used to solve the total PSM. To achieve a lower computational complexity, a maximum trace method, called Max-TR-SVD, is proposed by optimize the PSM of all IRSs. Numerical simulation results has shown that the proposed NSP-ZF-PA performs much better than Max-TR-SVD in terms of rate. In particular, the rate of NSP-ZF-PA with sixteen small IRSs is about five times that of NSP-ZF-PA with combining all small IRSs as a single large IRS. Thus, a dramatic rate enhancement may be achieved by multiple distributed IRSs.