user8157: Sn 2.1 has been translated as follows:

Ye ariyasaccāni vibhāvayanti,  Gambhīrapaññena sudesitāni;  Kiñcāpi te
  honti bhusaṃ pamattā,  Na te bhavaṃ aṭṭhamam ādiyanti; 
  Idampi saṅghe ratanaṃ paṇītaṃ,  Etena saccena suvatthi hotu
Who clearly comprehend these Noble Truths well-taught by him of wisdom
  fathomless, however heedless be they afterwards upon an eighth (aṭṭhamam)
existence (bhavaṃ) they’ll not seize (ādiyanti). Yea, in the Saṅgha is this glorious gem: By virtue of this truth, may blessing be! (Mills)
Those who have seen clearly the noble truths well-taught by the one of
  deep discernment — regardless of what [later] might make them heedless
  — will come to no eighth state of becoming.   This, too, is an
  exquisite treasure in the Sangha.     By this truth may there be
  well-being. (Thanissaro)
Those who realized the Noble Truths well taught by him who is profound
  in wisdom (the Buddha), even though they may be exceedingly heedless,
  they will not take an eighth existence (in the realm of sense
  spheres). This precious jewel is the Sangha. By this (asseveration of
  the) truth may there be happiness. (Piyadassi)

What is meant here by an "eighth grasping, seizing or taking up (ādiyati) of becoming/existence (bhava)"?

user254: I'm told that "the commentaries of multiple Indian Buddhist traditions (not just the Theravada)" define this kind of thing as referring to sotapanna having "seven more lives".
See e.g. How do you know what ‘sattakkhattuparama’ means?.
You ask, "What is meant?"
It's as "lives" (and so on) that a lot of people understand it and/or teach it -- and that is, arguably, what the text "says" -- even if you might say it doesn't "mean" what it seems to.
Perhaps you have a different interpretation of what "birth" and so on means -- and even, an interpretation which you can or want to justify, and which some other people (seem to) agree with.
I think I've read your suggesting, in the past, that the "seven" refers to "seven more fetters" -- and that "birth" and "becoming" and so on refer to the arising of self-views (e,g, identity views).
There's a Meta-topic, Questions asking for an answer to a controversy, where suggestions include,

Instead of changing question to be about controversy it is also possible to just outline controversy in the answer.

Anyway I think that this is (or e.g. that by posting about it as you do, you make it) controversial --and this answer is, what, meant to "outline" that controversy.
You'e written abut this topic at lot -- endlessly, it seems!

8157: <p>Sn 2.1 has been translated as follows:</p>

<blockquote>
  <p>Ye ariyasaccāni vibhāvayanti,  Gambhīrapaññena sudesitāni;  Kiñcāpi te
  honti bhusaṃ pamattā,  Na te <strong>bhavaṃ</strong> <strong>aṭṭhamam</strong> <strong>ādiyanti</strong>; 
  Idampi saṅghe ratanaṃ paṇītaṃ,  Etena saccena suvatthi hotu</p>
  
  <p>Who clearly comprehend these Noble Truths well-taught by him of wisdom
  fathomless, however heedless be they afterwards upon an <strong>eighth (aṭṭhamam)</strong>
  <strong>existence (bhavaṃ)</strong> they’ll not <strong>seize (ādiyanti)</strong>. Yea, in the Saṅgha is this glorious gem: By virtue of this truth, may blessing be! (Mills)</p>
  
  <p>Those who have seen clearly the noble truths well-taught by the one of
  deep discernment — regardless of what [later] might make them heedless
  — will come to no <strong>eighth state of becoming</strong>.   This, too, is an
  exquisite treasure in the Sangha.     By this truth may there be
  well-being. (Thanissaro)</p>
  
  <p>Those who realized the Noble Truths well taught by him who is profound
  in wisdom (the Buddha), even though they may be exceedingly heedless,
  they will not <strong>take an eighth existence</strong> (in the realm of sense
  spheres). This precious jewel is the Sangha. By this (asseveration of
  the) truth may there be happiness. (Piyadassi)</p>
</blockquote>

<p>What is meant here by an "eighth grasping, seizing or taking up (ādiyati) of becoming/existence (bhava)"?</p>
 254: <p>I'm told that "the commentaries of multiple Indian Buddhist traditions (not just the Theravada)" define this kind of thing as referring to sotapanna having "seven more lives".</p>

<p>See e.g. <a href="https://discourse.suttacentral.net/t/how-do-you-know-what-sattakkhattuparama-means/11131" rel="nofollow noreferrer">How do you know what ‘sattakkhattuparama’ means?</a>.</p>

<p>You ask, "What is meant?"</p>

<p>It's as "lives" (and so on) that a lot of people understand it and/or teach it -- and that is, arguably, what the text "says" -- even if you might say it doesn't "mean" what it seems to.</p>

<p>Perhaps you have a different interpretation of what "birth" and so on means -- and even, an interpretation which you can or want to justify, and which <em>some</em> other people (seem to) agree with.</p>

<p>I think I've read your suggesting, in the past, that the "seven" refers to "seven more <em>fetters</em>" -- and that "birth" and "becoming" and so on refer to the arising of self-views (e,g, identity views).</p>

<p>There's a Meta-topic, <a href="https://buddhism.meta.stackexchange.com/q/114/254">Questions asking for an answer to a controversy</a>, where suggestions include,</p>

<blockquote>
  <p>Instead of changing question to be about controversy it is also possible to just outline controversy in the answer.</p>
</blockquote>

<p>Anyway I think that this is (or e.g. that by posting about it as you do, you make it) controversial --and this answer is, what, meant to "outline" that controversy.</p>

<p>You'e written abut this topic at lot -- endlessly, it seems!</p>
