It has long been expected that a quantum field theory (QFT) “beyond the Standard Model” (SM) will eventually unify gravitation with particle interactions. Unfortunately, this “Theory of everything” remains elusive. Alternatively, full unification could be based on a philosophical concept termed hereby as the General Principle of Interaction (GPI), which extends the Einsteinian understanding of vacuum and matter proposing the spacetime geometry-based unification. Assuming that geometry of the four-dimensional (4D) spacetime governs only gravitational forces, a geometry-based description of other forces is possible only with the assumption of undetectable compact extra dimensions, e.g. Kaluza-Klein approach. The assumption of extra dimensions being compactified down to microscopic radii would explain their undetectability and quantization of the forces they govern. The fifth dimension compactified down to an atomic size would be sufficient to explain the electromagnetism with the 5D spacetime geometry. Further addition of a set of three extra dimensions compactified down to a nuclear size would explain the nuclear forces. The 8D spacetime containing hidden subspaces of compactified dimensions, the geometry of which governs forces other than gravitation, comprises the fractal spacetime concept (FSC). Surprisingly, this simple unification approach remains undeveloped. The GPI-based approach is expected to find a connection between the classical Kaluza-Klein theory and the two most fundamental QFTs, quantum electrodynamics (QED) and quantum chromodynamics (QCD). Generally, the leptons and photons should be understood as the elementary electric charge-induced wave-like 5D spacetime deformations with the “shadow” deformations (projections) in the ordinary 4D spacetime (induced masses); the quarks and gluons should be understood as the color charge-induced wave-like 8D spacetime deformations with the “shadow” deformations in the 5D spacetime (induced electric charges) and the “shadow” ordinary 4D spacetime deformations. The number of the fundamental field types should be reduced to three: strong, electroweak, and gravitational fields. The dark matter is hypothesized as the wave-like 4D spacetime deformations induced by yet unknown gravitational charges. The dark energy is the 4D spacetime background curvature defined by its size and shape. In general, it seems possible to describe all the four types of interaction with the fractal geometry of the multidimensional spacetime. However, the two methods (the GR and the SM) describing the two different geometries (large and compact, respectively) likely cannot be combined in a single unified framework.