It's fairly straightforward to expand the Price equation if you fix the genetic operators. This was done in one CS-oriented paper. Bassett et al. (2004) (preprint):
where k iterates over the genetic operators.
But it's not at all straightforward (and I suspect not possible) to do that for an all-encompassing abstract notion of evolvability (of every rule/mechanism that might be evolvable). I mean if the rules/operators are countable, you could write an infinite sum on the right hand side of that equation, but it's not clear how that helps with anything in practice.
If you use the multi-level (= group selection) version of the Price equation (as suggested in the other answer), you still have to decide (a priori) on grouping so basically enumerate over the (potentially evolvable) operators, albeit do that in terms of groups. For example, an operator can be recombination, which is the same as deciding to have groups for sexual and asexual organisms. I think the operator approach may be preferable in some cases because it can be real-valued (i.e. a continuous quantity). Although not using the (above) Price equation explicitly, such research on evolvability of specific (continuous) operators has been carried out, e.g. on the optimal recombination rate (Lobkovsky et al., 2016) etc.
On a different tack, and possibly closer to biology as a general idea, in another CS-oriented paper, Touissant (2003) proposed a (non-trivial) notion of embedding the evolvability of the parameters of interest into the "normal" genotype space.
In simple cases where the genotype space decomposes (strategy
parameters) an embedding space of neutral sets is obvious. To generalize to arbitrary neutral sets and arbitrary genotype-phenotype mappings we introduced the σ-embedding, i.e.,
we embedded neutral sets in the space of probability distributions over the genotype space
(exploration distributions). [...]
the question of how variational properties evolve has also been raised in numerous
variations (pleiotropy, canalization, epistatis, etc.) in the biology literature. These discussions aim at understanding how evolution can handle to introduce correlations or mutational
robustness or functional modularity in phenotypic exploration. Our answer is that variational properties evolve as to approximate the selection distribution. If, for example, certain
phenotypic traits are correlated in the selection distribution F, then the Kullback-Leibler
divergence decreases if these correlations are also present in the exploration distribution σ.
Alas he doesn't derive anything resembling a Price equation using his approach. (He does have a twin notion of evolution and σ-evolution, but there's no hierarchy/grouping.) Whether this notion is actually biologically useful, probably depends crucially on the embedding.
There are some papers in actual biology research that are closer to this idea of "embedded" evolvability. For example one paper (Lehman and Stanley, 2013) which looks at (actually defined evolvability in terms of) phenotypic variability.
one widely-held conception of evolvability as the capacity of an organism to “generate heritable phenotypic variation” [...], which is also the definition adopted in this paper. While evolvability is also sometimes discussed in relation to adaptation [...], the chosen definition reflects a growing consensus in biology that phenotypic variability in its own right deserves study in the context of evolvability
So this is one kind of concrete embedding. But no Price equation based on this idea that I could find in there...
On the other hand Rice (2008) does propose a stochastic extension of the Price equation, based on this idea that variability matters (or is all that there is to evolvability according to some):
A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness distributions contribute to directional evolution. Unfortunately the most general mathematical description of evolution that we have, the Price equation, is derived under the assumption that both fitness and offspring phenotype are fixed values that are known exactly. The Price equation is thus poorly equipped to study an important class of evolutionary processes. [...]
I present a general equation for directional evolutionary change that incorporates both deterministic and stochastic processes and applies to any evolving system. This is essentially a stochastic version of the Price equation [...]
This [new] equation shows that the effects of selection are actually amplified by random variation in fitness.
Finally, (as acknowledged in this latter paper) all variations on Price equation are over immediate successive generations. If you want to iterate forward (to infinity) you need to use a diffusion equation/model. (See chapter 7 in Durrett's book, for instance.)
