So, you really want to go further? The hyper-illions weren't enough for you? Fine. I introduce to you the Extended Hyper-Illions.
We start off with expansion, an extension to the hyper-operators by Jonathan Bowers.
Our next suffix is -ilexpion
Milexpion = 10{{1}}6
Bilexpion = 10{{1}}9
This is boring, next suffix.
-ilmultexpion
Milmultexpion = 10{{2}}6
Boring already. I'll just list the suffixes
-ilpowexpion
-iltetrexpion
Next up, explosion, notated by {{{1}}}
-ilexplion
-ilmultexplion
-ilpowexplion
-iltetrexplion
Detonation is next, {{{{1}}}}. I'll stop incrementing the inner part now.
-ildetonion >> {{{{1}}}}
Pentonation...
-ilpetonion >> {{{{{1}}}}}
Hexonation...
-ilhexonion >> {{{{{{1}}}}}}
Heptonation...
-ilheptonion >> {{{{{{{1}}}}}}}
Octonation...
-iloctonion >> {{{{{{{{1}}}}}}}}
Ennonation...
-ilennonion >> {1}^9
And finally, deconation.
-ildeconion >> {1}^10
Can we go further NOW?
Well, YES, but it's strange.
The next operation would be megotion, as Aarex Tiaokhiao called it.
However, there is not an official symbol in Unicode.
I'll attempt to try by using the square brackets.
-ilmegonion >> [1]
-ilmegoexpion >> [2]
-ilmegoexplion >> [3]
-ilmegodetonion >> [4]
-ilgigonion >> [[1]]
-ilgigoexpion >> [[2]]
-ilteronion >> [[[1]]]
-ilpetonion >> [[[[1]]]]
The next one, Aarex called "Hatotion", however "Exotion" would fit the previous ones better.
-ilexonion >> [[[[[1]]]]]
Because of the above reason, we will continue using the SI prefixes.
-ilzettonion >> [1]^6
-ilyottonion >> [1]^7
-ilronnonion >> [1]^8
-ilquettonion >> [1]^9
There is no SI prefix after quetta-, but Bowers' next -illion is the Hendillion, so we'll use that.
-ilhendonion >> [1]^10 = [[[[[[[[[[1]]]]]]]]]] (lots of square brackets)
Next is powiaination, but I'm too lazy to continue, so it ends off here. Goodbye!