I don't know if there is a googolplexplex (10 to the power of googolplex)
Yes, and it actually was originally called a googolplexplex, but it has been reformed as "googolduplex", in order to standardise the next orders, googoltriplex, googolquadplex (10^10^10^googol, 10^10^10^10^googol, respectively) ... googol-n-plex.
Once you get above a googoldecaplex (ten repetitions of "plex"), you get into googol-10^n-plex notation. Once you get into googolmilliplex (googol-1000-plex), you get into googol-10^3n-plex notation. And so on. [Note googolmilliplex, googol-10^3-plex, is 10^10^10^10...10^100. With 1000 10's raised to 10^100. Googolmegaplex, googol-10^6-plex, is 1,000,000 10's, raised to 10^100.)
Then you have "Great" numbers which are one power higher than their namesakes. Like "Great Googol", which is 10^101. Or "Great Googolplex", 10^(googol+1). And Googolbang or googol-factorial, (10^100)!, which is roughly 1.63 x googlplex^100 (1.6294... x 10^10^100^100. Interestingly, in spite of having a hundred googolplexes of digits, it only has 18 significant figures.)
These are, of course, only the smaller googol related numbers. At some point it really gets silly.