Is it possible to design a dynamical/adaptable functionally/logically complete circuit?
Any PLD, CPLD, or FPGA (three generations of programmable logic chips) has a programmable gate array that can emulate a wide range of logic functions.

In terms of a non-programmable, off-the-shelf chip, the closest thing probably is an AND-OR-Invert gate.

https://en.wikipedia.org/wiki/AND-OR-Invert