user8157: In this previous question, I listed the results of my investigations into how each nidana (link) in dependent origination appears to be 'singular', except 'sankhara', which is plural. 
The 'jati' ('birth') link also appears to be singular. However, what is unusual about it is the singular 'birth' that occurs appears to have 'plural' components. It is translated as follows by Bhikkhus Bodhi, Thanissaro & Sujato: 

Katamā ca, bhikkhave, jāti (singular)? Yā tesaṃ tesaṃ sattānaṃ (plural) tamhi tamhi sattanikāye (plural) jāti sañjāti okkanti abhinibbatti khandhānaṃ
  pātubhāvo āyatanānaṃ paṭilābho.
And what, bhikkhus, is birth? The birth of the various beings (sattānaṃ) into the various orders of beings, their being born, descent, production,
  the manifestation of the aggregates, the obtaining of the sense bases.
  This is called birth. (Bodhi)
And what is birth? Whatever birth, taking birth, descent, coming-to-be, coming-forth, appearance of aggregates, & acquisition of
  [sense] media of the various beings in this or that group of beings,
  that is called birth (Thanissaro).
The rebirth, inception, conception, reincarnation, manifestation of the aggregates, and acquisition of the sense fields of the various
  sentient beings in the various orders of sentient beings. (Sujato)

Now, each link of Dependent Origination appears to apply to the sense experience of an individual. Or, alternately, the Buddhaghosa interpretation over 3 lifetimes appears to be about the reincarnation of an individual. 
This being so, why does 'birth' ('jati'), seemingly a singular process, seem to refer to the birth (yā jati) of multiple beings (sattānaṃ) into the multiple orders/groups of beings (sattanikāye)? Why is the plural Pali word 'sattānaṃ' contained in the definition of what appears to be a singular process called 'jati' ('birth') in Dependent Origination?

user18: 
why does 'birth' ('jati'), seemingly a singular process, seem to refer to the multiple births of multiple beings into the multiple orders/groups of beings?

jāti is singular in the passage quoted, so it is not referring to multiple births. sattanikaye is also singular, so "in this or that group of beings".

Why is the plural Pali word 'sattānaṃ' contained in the definition of what appears to be a singular process called 'jati' ('birth') in Dependent Origination?

tesaṃ tesaṃ sattānaṃ is not an ordinary plural, the duplicated pronoun means "of these or those", so the whole phrase means "whatever birth (singular) in this or that being-group of these or those beings".
it were to mean "the multiple births of multiple beings" as you suggest, jāti would have to be plural, which it isn't; yā jāti refers to a singular birth.
The commentary to this clause says:

yā tesaṃ tesaṃ sattānan ti idaṃ “imesaṃ nāmā”ti niyamābhāvato sabbasattānaṃ pariyādānavacanaṃ.

Which I translated roughly as:

yā tesaṃ tesaṃ sattānaṃ: this phrase is the taking up completely of all beings, from not specifying "of these only"

In other words, it is used to make clear that birth is not specific to one or another group of beings, but refers to birth in any group of beings.
In summary, the entire phrase appears simply to be saying that birth refers to any of the many kinds of birth in any of the many groups of beings that exist.

8157: <p>In this previous <a href="https://buddhism.stackexchange.com/questions/30162/why-is-the-pali-word-sa%E1%B9%85kh%C4%81r%C4%81-in-dependent-origination-plural">question</a>, I listed the results of my investigations into how each nidana (link) in dependent origination appears to be 'singular', except 'sankhara', which is plural. </p>

<p>The 'jati' ('birth') link also appears to be singular. However, what is unusual about it is the singular 'birth' that occurs appears to have 'plural' components. It is translated as follows by Bhikkhus Bodhi, Thanissaro &amp; Sujato: </p>

<blockquote>
  <p><em>Katamā ca, bhikkhave, jāti (singular)? Yā tesaṃ tesaṃ sattānaṃ (plural) tamhi tamhi sattanikāye (plural) jāti sañjāti okkanti abhinibbatti khandhānaṃ
  pātubhāvo āyatanānaṃ paṭilābho.</em></p>
  
  <p><em>And what, bhikkhus, is birth? The birth of the various <strong>beings</strong> (<strong>sattānaṃ</strong>) into the various orders of beings, their being born, descent, production,
  the manifestation of the aggregates, the obtaining of the sense bases.
  This is called birth. (Bodhi)</em></p>
  
  <p><em>And what is birth? Whatever birth, taking birth, descent, coming-to-be, coming-forth, appearance of aggregates, &amp; acquisition of
  [sense] media of the various beings in this or that group of beings,
  that is called birth (Thanissaro).</em></p>
  
  <p><em>The rebirth, inception, conception, <strong>reincarnation</strong>, manifestation of the aggregates, and acquisition of the sense fields of the various
  sentient beings in the various orders of sentient beings. (Sujato)</em></p>
</blockquote>

<p>Now, each link of Dependent Origination appears to apply to the sense experience of an individual. Or, alternately, the Buddhaghosa interpretation over 3 lifetimes appears to be about the reincarnation of an individual. </p>

<p>This being so, why does 'birth' ('jati'), seemingly a singular process, seem to refer to the birth (yā jati) of multiple beings (sattānaṃ) into the multiple orders/groups of beings (sattanikāye)? Why is the plural Pali word 'sattānaṃ' contained in the definition of what appears to be a singular process called 'jati' ('birth') in Dependent Origination?</p>
 18: <blockquote>
<p>why does 'birth' ('jati'), seemingly a singular process, seem to refer to the multiple births of multiple beings into the multiple orders/groups of beings?</p>
</blockquote>
<p><em>jāti</em> is singular in the passage quoted, so it is not referring to multiple births. <em>sattanikaye</em> is also singular, so &quot;in this or that group of beings&quot;.</p>
<blockquote>
<p>Why is the plural Pali word 'sattānaṃ' contained in the definition of what appears to be a singular process called 'jati' ('birth') in Dependent Origination?</p>
</blockquote>
<p><em>tesaṃ tesaṃ sattānaṃ</em> is not an ordinary plural, the duplicated pronoun means &quot;of these or those&quot;, so the whole phrase means &quot;whatever birth (singular) in this or that being-group of these or those beings&quot;.</p>
<p>it were to mean &quot;the multiple births of multiple beings&quot; as you suggest, <em>jāti</em> would have to be plural, which it isn't; <em>yā jāti</em> refers to a singular birth.</p>
<p>The commentary to this clause says:</p>
<blockquote>
<p><strong>yā tesaṃ tesaṃ sattānan</strong> ti idaṃ “imesaṃ nāmā”ti niyamābhāvato sabbasattānaṃ pariyādānavacanaṃ.</p>
</blockquote>
<p>Which I translated roughly as:</p>
<blockquote>
<p><strong>yā tesaṃ tesaṃ sattānaṃ</strong>: this phrase is the taking up completely of all beings, from not specifying &quot;of these only&quot;</p>
</blockquote>
<p>In other words, it is used to make clear that birth is not specific to one or another group of beings, but refers to birth in any group of beings.</p>
<p>In summary, the entire phrase appears simply to be saying that birth refers to any of the many kinds of birth in any of the many groups of beings that exist.</p>
