The 100 at the end is replaced with a larger power of 10 or added to 100. The suffix is placed at the end of the word.

Modifiers:

Googolspeck - 10↑90 | Subtract 10 from the exponent

Googolteen - 10↑100 +10 | Add 10 to the number

Googolty - 10↑101 | Add 1 to the exponent

Googolswarm - 10↑110 | Add 10 to the exponent

Power of 10:

Googolding - 10↑500 / 10↑(5x10↑3)

Googolchime - 10↑1,000 / 10↑10↑3

Googolbell - 10↑5,000 / 10↑(5x10↑4)

Googoltoll - 10↑10,000 / 10↑10↑4

Googolgong - 10↑100,000 / 10↑10↑5

Googolbong - 10↑100,000,000 / 10↑10↑8

Googolthrong - 10↑100,000,000,000 / 10↑10↑11

Googolgandigan - 10↑100,000,000,000,000 / 10↑10↑14 (another name is Googolquadrigong)

Googolquintigong - 10↑(100 quadrillion) / 10↑10↑17

Googolsextigong - 10↑(100 quintillion) / 10↑10↑20

Googolseptigong - 10↑(100 sextillion) / 10↑10↑23

Googoloctigong - 10↑(100 septillion) / 10↑10↑26

Googolnonigong - 10↑(100 octillion) / 10↑10↑29

Googoldecigong - 10↑(100 nonillion) / 10↑10↑32

You can continue the pattern using the prefixes from the Big zillions page if you want.

The 100 is replaced by nests of Googols (or stronger variants) at the end. These are placed at the end of the word, with the suffixes placed after the -plex part with an i.

Googolplex - 10↑10↑100 (the only extension officially recognized)

Googolplexichime - 10↑10↑1,000

Googolplexitoll - 10↑10↑10,000

Googolplexigong - 10↑10↑100,000

Googolplexibong - 10↑10↑100,000,000

Googolduplex - 10↑10↑10↑100 (also kind of well-recognized as Googolplexian) / (10↑)^3 100

Googoltriplex - 10↑10↑10↑10↑100 / (10↑)^4 100

Googolquadriplex - 10↑10↑10↑10↑10↑100 / (10↑)^5 100

Googolquintiplex - 10↑10↑10↑10↑10↑10↑100 / (10↑)^6 100

Googolsextiplex - (10↑)^7 100 (7 10s)

Googolseptiplex - (10↑)^8 100 (8 10s)

Googoloctiplex - (10↑)^9 100 (9 10s)

Googolnoniplex - (10↑)^10 100 (10 10s)

Googoldeciplex - (10↑)^11 100 (11 10s)

Again, you can continue this with prefixes from the Big zillions page if you want.

The number of arrows in Knuth's Up-Arrow notation increments with each new entry. The number in the bracket of Operator Notation and the third entry of Linear Array Notation (Bower's Exploding Array Function / Bird's Array Notation) are also considered here.

Giggol - 10↑↑100 / 10{2}100 / {10, 100, 2}

Giggolchime - 10↑↑1,000 / 10{2}1,000 / {10, 1,000, 2}

Giggoltoll - 10↑↑10,000 / 10{2}10,000 / {10, 10,000, 2}

Giggolgong - 10↑↑100,000 / 10{2}100,000 / {10, 100,000, 2}

Giggolbong - 10↑↑100,000,000 / 10{2}100,000,000 / {10, 100,000,000, 2}

Giggolplex - 10↑↑10↑↑100 / 10{2}10{2}100 / {10, {10, 100, 2}, 2}

Giggolduplex - 10↑↑10↑↑10↑↑100 / 10{2}10{2}10{2}100 / {10, {10, {10, 100, 2}, 2}, 2}

Gaggol - 10↑↑↑100 / 10{3}100 / {10, 100, 3}

Geegol - 10↑↑↑↑100 / 10{4}100 / {10, 100, 4}

Gigol - 10↑↑↑↑↑100 / 10{5}100 / {10, 100, 5}

Goggol - 10↑↑↑↑↑↑100 / 10{6}100 / {10, 100, 6}

Gagol - 10↑↑↑↑↑↑↑100 / 10{7}100 / {10, 100, 7}

Gocgol - 10↑↑↑↑↑↑↑↑100 / 10{8}100 / {10, 100, 8}

Gengol - 10↑↑↑↑↑↑↑↑↑100 / 10{9}100 / {10, 100, 9}

Gexgol - 10{10}100 / {10, 100, 10}

Gelgol - 10{11}100 / {10, 100, 11} (my name)

Gozengol - 10{12}100 / {10, 100, 12} (my name)

This tier only has a limited number of extensions. However, if you are clever, you could define new names past this.

The 100 is shifted to the right by an entry in Bower's Exploding Array Function / Bird's Array Notation, and a ten takes its place. Each added 10 affects the Latin prefix.

Boogol - {10, 10, 100} / 10{100}10

Boogolchime - {10, 10, 1,000} / 10{1,000}10

Boogoltoll - {10, 10, 10,000} / 10{10,000}10

Boogolgong - {10, 10, 100,000} / 10{100,000}10

Boogolbong - {10, 10, 100,000,000} / 10{100,000,000}10

Boogolplex - {10, 10, {10, 10, 100}} / 10{10{100}10}10

Boogolduplex - {10, 10, {10, 10, {10, 10, 100}}} / 10{10{10{100}10}10}10

Biggol - {10, 10, 100, 2} / 10{{100}}10

Baggol - {10, 10, 100, 3} / 10{{{100}}}10

Beegol - {10, 10, 100, 4} / 10{{{{100}}}}10

Bigol - {10, 10, 100, 5} / 10{{{{{100}}}}}10

Troogol - {10, 10, 10, 100}

Quadroogol - {10, 10, 10, 10, 100}

Quintoogol - {10, 10, 10, 10, 10, 100}

Sextoogol - {10, 10, 10, 10, 10, 10, 100}

Septoogol - {10, 10, 10, 10, 10, 10, 10, 100}

Octoogol - {10, 10, 10, 10, 10, 10, 10, 10, 100}

Nonoogol - {10, 10, 10, 10, 10, 10, 10, 10, 10, 100}

Decoogol - {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 100}

This can continue for as long as the prefixes from the Big zillions page allow.

The number on the right of the dimensional nest of BEAF and BAN dictates the entry of this tier.

Goobol - {10, 100 [2] 2} / {10, 100 (1) 2}

Goobolchime - {10, 1,000 [2] 2} / {10, 1,000 (1) 2}

Gooboltoll - {10, 10,000 [2] 2} / {10, 10,000 (1) 2}

Goobolgong - {10, 100,000 [2] 2} / {10, 100,000 (1) 2}

Goobolplex - {10, {10, 100 [2] 2} [2] 2} / {10, {10, 100 (1) 2} (1) 2}

Goobolduplex - {10, {10, {10, 100 [2] 2} [2] 2} [2] 2} / {10, {10, {10, 100 (1) 2} (1) 2} (1) 2}

Gibbol - {10, 100, 2 [2] 2} / {10, 100, 2 (1) 2}

Gabbol - {10, 100, 3 [2] 2} / {10, 100, 3 (1) 2}

Geebol - {10, 100, 4 [2] 2} / {10, 100, 4 (1) 2}

Gibol - {10, 100, 5 [2] 2} / {10, 100, 5 (1) 2} (rest of tier 3 is same)

Boobol - {10, 10, 100 [2] 2} / {10, 10, 100 (1) 2}

Troobol - {10, 10, 10, 100 [2] 2} / {10, 10, 10, 100 (1) 2}

Quadroobol - {10, 10, 10, 10, 100 [2] 2} / {10, 10, 10, 10, 100 (1) 2}

Gootrol - {10, 100 [2] 3} / {10, 100 (1) 3}

Gitrol - {10, 100, 2 [2] 3} / {10, 100, 2 (1) 3}

Gatrol - {10, 100, 3 [2] 3} / {10, 100, 3 (1) 3}

Geetrol - {10, 100, 4 [2] 3} / {10, 100, 4 (1) 3}

Gietrol - {10, 100, 5 [2] 3} / {10, 100, 5 (1) 3}

Gotrol - {10, 100, 6 [2] 3} / {10, 100, 6 (1) 3}

Gaitrol - {10, 100, 7 [2] 3} / {10, 100, 7 (1) 3} (rest of tier 3 is same)

Bootrol - {10, 10, 100 [2] 3} / {10, 10, 100 (1) 3}

Trootrol - {10, 10, 10, 100 [2] 3} / {10, 10, 10, 100 (1) 3}

Quadrootrol - {10, 10, 10, 10, 100 [2] 3} / {10, 10, 10, 10, 100 (1) 3}

Gooquadrol - {10, 100 [2] 4} / {10, 100 (1) 4}

Gooquintol - {10, 100 [2] 5} / {10, 100 (1) 5}

Goosextol - {10, 100 [2] 6} / {10, 100 (1) 6}

Gooseptol - {10, 100 [2] 7} / {10, 100 (1) 7}

Goooctol - {10, 100 [2] 8} / {10, 100 (1) 8}

Goononol - {10, 100 [2] 9} / {10, 100 (1) 9}

Goodecol - {10, 100 [2] 10} / {10, 100 (1) 10}

You could continue this (for the fourth time) with prefixes from the Big zillions page.

The 100 is on the righthand side of the dimensional nests of BEAF and BAN.

Like the heading says, there is only one prefix here. Tier 5 is ignored here and Tier 4 has an extra step here.

Gossol - {10, 10 [2] 100} / {10, 10 (1) 100}

Gossolchime - {10, 10 [2] 1,000} / {10, 10 (1) 1,000}

Gossoltoll - {10, 10 [2] 10,000} / {10, 10 (1) 10,000}

Gossolgong - {10, 10 [2] 100,000} / {10, 10 (1) 100,000}

Gossolplex - {10, 10 [2] {10, 10 [2] 100}}

Gossolduplex - {10, 10 [2] {10, 10 [2] {10, 10 [2] 100}}}

Gissol - {10, 10 [2] 100, 2}

Gassol - {10, 10 [2] 100, 3}

Geesol - {10, 10 [2] 100, 4}

Gussol - {10, 10 [2] 100, 5}

Goosol - {10, 10 [2] 100, 6}

Gasol - {10, 10 [2] 100, 7}

Mossol - {10, 10 [2] 10, 100}

Bossol - {10, 10 [2] 10, 10, 100}

Trossol - {10, 10 [2] 10, 10, 10, 100}

Quadrossol - {10, 10 [2] 10, 10, 10, 10, 100}

The dimensional nest number of BEAF and BAN increments with each new entry.

This is where most extensions made by me lie in.

Goxxol - {10, 100 [3] 2} / {10, 100 (2) 2}

Goxxolchime - {10, 1,000 [3] 2} / {10, 1,000 (2) 2}

Goxxolplex - {10, {10, 100 [3] 2} [3] 2} / {10, {10, 100 (2) 2} (2) 2}

Gixxol - {10, 100, 2 [3] 2} / {10, 100, 2 (2) 2}

Boxxol - {10, 10, 100 [3] 2} / {10, 10, 100 (2) 2}

Gooboxxol - {10, 100 [2] 2 [3] 2} / {10, 100 (1) 2 (2) 2}

Gossoxxol - {10, 10 [2] 100 [3] 2} / {10, 10 (1) 100 (2) 2}

Gotraxxol - {10, 100 [3] 3} / {10, 100 (2) 3}

Goquaxxol - {10, 100 [3] 4} / {10, 100 (2) 4}

Gosxol - {10, 10 [3] 100} / {10, 10 (2) 100}

Goxxoobol - {10, 100 [3] 1 [2] 2} / {10, 100 (2)(1) 2}

Boxxoobol - {10, 10, 100 [3] 1 [2] 2} / {10, 10, 100 (2)(1) 2}

Gooboxxoobol - {10, 100 [2] 2 [3] 1 [2] 2} / {10, 100 (1) 2 (2)(1) 2}

Goxxibbol - {10, 100 [3] 2 [2] 2} / {10, 100 (2) 2 (1) 2}

Goxxabbol - {10, 100 [3] 3 [2] 2} / {10, 100 (2) 3 (1) 2}

Goxgoobol- {10, 10 [3] 100 [2] 2} / {10, 10 (2) 100 (1) 2}

Goxmoobol- {10, 10 [3] 10, 100 [2] 2} / {10, 10 (2) 10, 100 (1) 2}

Goxboobol- {10, 10 [3] 10, 10, 100 [2] 2} / {10, 10 (2) 10, 10, 100 (1) 2}

Goxxootrol - {10, 100 [3] 1 [2] 3} / {10, 100 (2)(1) 3}

Goxossol - {10, 100 [3] 1 [2] 100} / {10, 100 (2)(1) 100}

Goxmossol - {10, 100 [3] 1 [2] 10, 100} / {10, 100 (2)(1) 10, 100}

Govtrol - {10, 100 [4] 2} / {10, 100 (3) 2}

Govteel - {10, 100 [5] 2} / {10, 100 (4) 2}

Govpeel - {10, 100 [6] 2} / {10, 100 (5) 2}

Govexel - {10, 100 [7] 2} / {10, 100 (6) 2}

Goveptel - {10, 100 [8] 2} / {10, 100 (7) 2}

Govoctel - {10, 100 [9] 2} / {10, 100 (8) 2}

Govenel - {10, 100 [10] 2} / {10, 100 (9) 2}

Govdecel - {10, 100 [11] 2} / {10, 100 (10) 2}