What are some other classes of data.frame?

I know of (base? classic?) data.frame, data.table, and tibble.

What other classes satisfy is.data.frame? (Obviously any can be constructed, so perhaps I want answers limited to those established in a package on CRAN.)

This is an implementation of is.data.frame:

function (x) 
inherits(x, "data.frame")
<bytecode: 0x5586f8758948>
<environment: namespace:base>

As you can see, it will return TRUE only if your object has a class data.frame. What data.table and tibble do is they extend data.frame class. Concretely:

x <- data.frame(a = rnorm(10))
#> [1] "data.frame"

#> [1] "data.table" "data.frame"

#> [1] "tbl_df"     "tbl"        "data.frame"

Created on 2018-08-31 by the reprex package (v0.2.0).