Formal alternative for "on the other hand, ... on the other other hand ..."

Question

On Stack Exchange, I sometimes come across argument constructions that follow the pattern

(On (the) one hand ...) On the other hand, ... On the other other hand, ...

The argument construction "On (the) one hand ... On the other hand, ..." is perfect for contrasting two arguments, objects, etcetera. However, since I don't have prehensile feet, the addition of "on the other other hand ..." seems rather unnatural to me. On Science Fiction and Fantasy Stack Exchange, some people say "on the gripping hand", but that sounds just as unnatural to me.
Is there an alternative to this linguistic Mexican standoff that can be used in formal contexts such as academic papers?
Below is an example from Cross Validated SE (emphasis mine):

I usually follow hierarchy but depart from it in some situations. (...)
On the other hand, you might still want to test for a speed effect because it might indicate that "break-in" effects differ at different speeds. On the other other hand, an even better way to handle break-in would be to get data at zero and at very low mileage and then test for non-linearity. Note that removing the intercept term can be thought of as a special case of violating hierarchy.

Below is an example from Just putting it out there: I still buy MP3s by Georgina Ustik on TNW (18 August 2019) (emphasis mine):

Artists are making more money on tour and via brand partnerships, something they can get through the seamless webbed relationship between streaming platforms and social media, than ever before. On the other hand, algorithms amplify music that’s already picking up steam, so it’s easy for new music and smaller artists to get lost in the ever-growing crowd.

But on the other OTHER hand, streaming platforms stopped the rise in music piracy à la sites like Napster, because of its higher quality and the promises of AI-driven suggestions, so they kind of saved the industry. But on the other OTHER OTHER hand, it’s now being reported that thanks to too many streaming service options, piracy is getting hot again.

Other examples can be found on Mathematics Stack Exchange (four hands), Electrical Engineering SE (four hands), Database Administrators SE (four hands, with commas between "other"), Open Source SE (just three hands), Meta Stack Exchange (three hands), User Experience Stack Exchange (three hands) and Academia Stack Exchange (three hands).
I am looking for an alternative construction that fits such long lists of "contrasts" and that can be used in formal writing.

Edwin Ashworth · Answer

And then again or but then again are a pair of very idiomatic additive or contrastive / mitigating pragmatic markers, useful because it can be used in all but ultra-formal registers.
If these are considered inappropriate, you may well be left with

'A third alternative is [to] ...' / 'Yet another alternative is ...'.

You're really into formatting lists of complex items here, and bullet points or paragraphing, perhaps with the common ordering markers (Third/ly, ... Finally, ) are the usual ways of handling this.
As an aside, there is a paper discussing the effectiveness of, and construing mechanisms in play in typical readers when meeting, the contrastive marker pair 'on the one hand ... on the other hand' ...  by Scholman, Rohdeb and Demberg at Science Direct_Journal of Memory and Language. The only other contrastives they mention are but and though, obviously not appropriate here.
A problem with the contrastive (as opposed to the mere listing of associated elements, when there are far better alternatives) usage of OT1H ... OTOH ... OTOOH ... ... ) is that clarity is soon lost. The first case is obviously [A; nevertheless, B]. But then, with the 'third hand', we have to decide whether C is in spite of just A, A and B, or just B. What is the three-handed vehicle of the metaphor?

fev · Answer

If you wish to enumerate several aspects that are in contrast with the same issue or idea in a structure that would look something like this

A but (B, and C and D etc...)

you might as well indicate that such an enumeration is coming by using phrases or words like by contrast, nevertheless, however:

However, there are some aspects that point into a different/opposite direction. Firstly... Secondly... Thirdly...

Or you could replace firstly, secondly, etc. with furthermore, moreover, additionally
If, erm... on the other hand (!), the aspects mentioned are contrasting one another, and not the same issue, than you have a structure like:

A but B [but C (but D)] etc. (of course, other combinations could be possible, too)

then you might play with words like:

A. [However, (while/whilst B...,) C...] Yet, D... Despite all that, E... Having said all that, F...

You can include and exclude your aspects into or out of contrasting groups, according to the connections that exist among them.
Certainly, instead of "however" you can use any synonym that is more to your liking. I am quite picky in writing as well. WordHippo might help you with your word choice.

Formal alternative for "on the other hand, ... on the other other hand ..."

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