In this article we have described a multiproduct model of economical dynamics of Gale type, in which the changes in production technology (the dynamics of Gale type production spaces) depend upon the scale of targeted investments. Under such assumptions we have proved a so-called “weak” version of a multilane turnpike theorem in the Gale type economy with varying technology which converges to a certain limit technology. It states that in the long periods of time, regardless of the initial state of the economy, the optimal growth processes almost always lie close to the family of steady growth paths with maximum growth rate called the multilane turnpike.