Note that power and ground planes meet that definition, as the planes are bypassed together in various locations with capacitors.
In fact, aside from heavy loads (large bus drivers, CPUs/FPGAs?), the location of bypass caps is largely irrelevant, and they can be sprinkled evenly around the planes. Probably with some savings on parts count too (compared to automatically bypassing every single power pin)!
Even if not bypassed, we can always ask: how much? The description sounds plausible (signals bouncing around between planes), so let's do a reality check and see what magnitude we expect from it. Well, the plane is a low impedance transmission line, so for very short signals, we don't expect much funny business; even crossing over gaps between planes (such as from one VCC domain to another -- note, not gaps across ALL planes: there must still be at least one contiguous (preferably GND) plane at any such crossing!), the image current sneaks under the edge of one plane and immediately pops up from the other; between planes, that current fans out broadly, the characteristic impedance dropping quickly with time. So, it's effectively like there's a hairpin loop in the trace, as if it rose up away from the plane (like a one-turn air core inductor). This is an impedance discontinuity, but a brief one, permissible for many digital buses, including PCIe (also, as long as it manifests common-mode, it's fine for differential pairs). Much faster (10s ps?), or precise, signals will want to avoid this kind of environment, of course.
So it might be fine for functional operation, or signal quality. That's one signal with respect to its transmitter and receiver. Is it fine for emissions or immunity (external transmitters or receivers)?
About that current which fans out between planes: It will eventually find some bypass caps, reflect off them (because the vias, traces and cap bodies act as shorting loops), and so on and so forth, the wavefront scattering and dissipating over time. When impedances are matched and well damped, the dissipation dominates, and the planes go.. "thud". Some disturbance might be sensible elsewhere (say on other power pins), but it will likely be small, and brief. We can draw the equivalent circuit, between the signal trace impedance, plane impedance, bypass caps and other supply impedances, and calculate how much ripple will be produced. Or measure it the same way (being careful to get a very solid ground for our probe, to rule out common mode influence -- we're talking mV here!).
Likewise, a poorly terminated plane might end up resonating against poorly chosen or placed bypass caps, and in that case the whole plane pair acts as a patch dipole antenna, potentially quite an effective radiator at high frequencies (say 100MHz+, with an asymptotic tail at low frequencies where the board is electrically small and thus a poor radiator but still a radiator nonetheless, given a strong enough noise source!).
Conversely, a plane pair acts as an antenna, picking up whatever ambient noise is present. If its impedance is low at all frequencies, it acts as an effective impedance divider (or weirder things when wavelengths get involved) to those fields, coupling poorly to them. Whereas an accidentally resonant plane will have an impedance peak, that can couple much more strongly.
These are all reciprocal systems of course, so whenever a structure is a good transmitter, it is also a good receiver. Technically, I don't have to enumerate all these conditions, but brains are weird, and it can help to remind ourselves of these facts lest we forget them...at our own expense.
Tim