Almost all combining rules (including skin tone modifiers) require a zero-width joiner character between the person emoji and the modifier emoji. So really it's frowning face + ZWJ + brown texture = brown frowning face. (Although technically I don't think frowning face can be modified.) Also, there are relatively few ZWJ combinations.
Technically, there are some older combination emojis that predate ZWJ, mainly the flags, which are composed of two single-letter emojis, e.g. regional-indicator-U + regional-indicator-S = United States flag. So I guess it might be possible to get a couple of those.
And in any case, I think this page assumes that you're staying within the bounds of the basic multilingual plane (it mentions a self-inverting transform would be ROT32768), which doesn't include emojis or skin tone modifiers.