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From the question: "[How does the use of いかんによっては in this question determine
one answer over another?](https://japanese.stackexchange.com/q/7035/542)", it
is observed that:

  * The use of によって means to change state or behaviour depending on, or according to something. It expresses variety.
  * The use of によっては pinpoints one outcome from a range of possible outcomes.

While the previous question deals with appropriate usage determination, this
question seeks to understand the underlying principle governing it.

**(Question) Why does the presence of は do this, and how does this link back
to what we know of は?**

What I typically know of the particle は, is that it is a disambiguative
particle and has thematic and contrastive roles.
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grammar particle-は
How does は apply itself to によっては?
I think you've picked up on my explanation, which was taken from 新完全マスター文法N3,
日本語表現文型辞典 so, as I do find the expression with は intuitive/natural, I should
expand on my previous answer.

The definitions were:

> によって：means to change state or behaviour depending on something or according
> to something. It expresses variety and is often used with さまざまだ and かえる.
>
> によっては：pinpoints one outcome from a range of possible outcomes.

Sentences given in the book applying によって are:

> 国によって習慣が違う
>
> 感じ方は人によって様様だ。

One sample sentence in the N1 book pinpointing a single outcome using によっては
was:

> 私の帰宅時間は毎日違う。日によっては夜中になることもある。
>
> I get home at a different time every day. Some days I get even home in the
> middle of the night.

A similar sentence to this last sentence applying the same principles used in
the first two sentences to express variety using によって would be:

> 私の帰宅時間は日によって違う。 The time I get home varies from day to day.

If we work backwards, taking the last last sentence as the starting point and
then seek to pin point one result, taking "as for" as a crude translation of は
then we would say:

> Every day I get home at a different time. " **As for** some days, depending
> on the day itself", I even get home in the middle of the night.

Which takes us back to the sample sentence of によっては with what I hope is a
crude but reasonable explanation of how は is used not just in this expression
but in a manner that is consistent with some of its normal uses
(raising/drawing attention to/ emphasising a topic)

Consider also other ～ては structures:

  * ～については
  * ～に関しては

BによってA is used in sentences to make statements such as "A varies, depending on
B".  
BによってはC is used to make statements such as "As for all possible results
dependent on B, C can happen", C being a member of set A.  
は selects Bによって as a topic for further discourse, similar to ～については and
～に関しては.
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は simply focuses the sentence and marks the subject and makes it stand out as
the primary causal factor in the sentence. It's similar to how you would say
私は but instead of a person subject you have an non-noun (e.g. event or other
factor) focus of the sentence.

(Answer much shorter than others but I think it wraps it up well)
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