First of all EEQT itself needs to be further developed in order to provide a theoretical and computational answer to the needs of modern quantum engineering
and technology. We need to include classical systems with infinite
numbers of degrees of freedom - like electromagnetic and/or gravitational
field. We also need to include infinite quantum systems so as
to understand and simulate Bose gas and its phase transitions. But, there
are also steps that must be taken far beyond the paradigm of EEQT.
As we have emphasized so many times: quantum theory has yet to be understood in terms of a "non-linear classical theory." But what we mean by a "classical theory" is something much more advanced and more general than clasical mechanics or classical field theory. By a "classical theory" we mean first of all, a theory that is not based on probabilities from the start; a theory in which probabilities appear at a later stage, derived from the theory; derived perhaps, in a necessary way. Such a theory must not only specify the mathematical objects and their relations but also make "predictions".
A classical theory is, in particular, a theory in which discrete events can happen, events that are "objective." They may be events that affect mainly the physical stratum, but they may be also "mental events," changes of states of "consciousness;" whatever they are, even if they are concerned with branchings of universes, - they DO HAPPEN.
Such a theory, encompassing the quantum theory as we know it today, does not yet exist, but we can envisage its possible shape. Nothing serves better than an example, so let us give here an example of how such a theory can be construed.
Imagine a theory developed a'la Einstein's unified field theory, but with variable metric signature, possibly with a complex causal web, multiple Einstein-Rosen  (see also ) bridges, time loops, nondifferrentiability, fractal structure, all of that additionally complicated by variable dimensionality of space and of "time" (cf . Imagine such a theory to be able to accomodate all the four fundamental forces known to us, but it also involves an extra field, which is different from physical fields, and which is non-local in the sense that it does not survive taking a macro-average-limit when causal space-time structure of Einstein's general relativity is recovered. This extra field would be a place for "thought forms" and our theory would couple these thought forms to more "physical" levels of reality. The very concept of "time" would arise only in one particular limiting structure. Nothing prevents a theory of such a type to have mathematical structures rich enough to accomodate consciousness and mind. Due to its complexity, density of time-loops, bubble-like causal structure, making predictions in such theory is possible only by applying probability - as it is the case with systems evolving according to deterministic but chaotic dynamics. Quantum wave function would emerge in such a theory as an effective way of predicting. That type of explanation of quantum indeterminism was postulated long ago by I. J. Good. In  he speculated that quantum indeterminism can be understood if we admit that individual quantum events that actually happen here and now have future advanced causes as well has past retarded causes.
A glimpse of such a thought may have occured to Alan Turing when he wrote his famous, already quoted sentence: "prediction must be linear, description must be nonlinear."
A theory going partially in this direction is being developed by L. Nottale  who states the observation, attributed to Feynman, that "the typical paths of quantum mechanical particles are continuous non-differentiable." Then he continues his development of fractal space-time ideas to conclude with: "The quantum behavior becomes, in this theory, a manifestation of the fractal geometry of space-time, in the same way gravitation is, in Einstein's theory of general (motion-)relativity, a manifestation of the curvature of space-time.
Another step in this direction comes from the work of Russian scientists - which started with the most original ideas of N.A. Kozyrev  and A. Sakharov , and is being developed in Moscow, the Urals and Siberia, see e.g. [46, 47, 48].