В каком-то из многих возможных контекстов, учитывая стилевые особенности текста, может означать и "влезть в разговор". Или лучше "вклиниться", чтобы не выражаться, как базарная баба...

https://wesbos.com/get-the-most-out-of-conferences/
https://www.allearsenglish.com/english-conversation-confident/

Очень похоже. Сама «кинематика» глагола jump такую возможность как бы подразумевает. Не говоря уже о вашем контексте, в котором это прямо проговаривается:

Being Effective on Televison
…
…
Jump into the conversation if you want to clarify a point or add to the conversation. Don't wait for the host to recognize you, but don't behave rudely.

Мне лично из вариантов больше всего понравилось употребленное вами же (когда вы не «искали эквивалент», а просто описывали это своими словами) вступать:

вступайте в разговор (если вы считаете необходимым что-то уточнить или заметить, не ждите, пока модератор предоставит вам слово)

*отзывы на кинопоиске: https://www.kinopoisk.ru/film/82425/#

You haven't given much context as Rus_Land says, but in your example:
* the person is clearly being invited to 'jump' into the conversion; and
* it isn't being used disapprovingly,
so I would treat 'jump into' as meaning simply 'join'. There's very little difference between the two in your example.

ваш стопарик (стопка выражений) больше, у меня было только 4:
1) join a conversation 2) get into a conversation
3) jump into a conversation 4) worm oneself into a conversation :)

ps. мне лично нравится пример с кинематикой, как разносторонний подход к пониманию вопРоса
pps. кстати, и о творчестве Вернера Херцога вспомнили, вот

Ralana: The link you've given contains no more information on context than your initial question does, ie none. That's because the quotation in your link is taken, in turn, from another, larger (original) document (which 00002 obviously found at 12:43 and which I've also now found after googling it):
http://www.au.af.mil/au/awc/awcgate/state/interviews.htm
This original document gives all of the context.

Your quote doesn't refer to everyday conversations at all; it's from a document giving public relations-type advice to:
* people who are likely to take part in 'round table'-type TV panel discussions about a subject; and
* people who are likely to be interviewed on TV about a subject at the same time as one or more other people
– as often happens, for example, on TV news channels where a host/programme presenter interviews two or more people with differing/opposing views about a subject.

'Jump into the conversation' here simply means 'interrupt the conversation taking place between:
* other members of the panel or
* the host (=programme presenter/chairman) and the other interviewee'
as appropriate, depending on the programme's format.

In future please give the full context at the very beginning.

johnstephenson,
1. запрос топика был не в том, чтобы найти всевозможные примеры-иллюстрации по разным ссылкам. Но в понимании диапазона значений этого широкоупотребимого выражения. С этим мы благополучно разобрались.
Ваше предположение о ссылке-источнике, которую я привела выше ошибочно.

Обычно в подобного рода высказывания-гипотезах при диалоге двух взрослых малознакомых людей принято добавлять прилагательные и вводные конструкции "по-видимому", "я так думаю" и пр.
В противном случае, это довольно часто звучит, как беспочвенное обвинение и попытка спровоцировать конфликтную ситуацию.

2. Приведённая ссылка в вашем посте не открывается.

I'm sorry if you disliked the tone of my last comment. I was simply trying to explain that 'to jump into (a/the) conversation' isn't a set expression; the exact meaning depends on the context, register etc, as Rus_Land, 00002 and others tried to explain. Unfortunately, if you don't know the context in which something's written, other people can't know it either; they can only guess at it.

Unfortunately the link you provided gave no more information than the sentence you'd already posted, so the link gave no context either. However, if you google your whole sentence (as 00002 did and I later did), you'll find that it's originally from a section entitled 'Being Effective on Television' in a document giving advice to journalists and others on how to communicate. The original document has then been copied by half-a-dozen other websites:

http://www.google.co.uk/search?as_q="Jump+into+the+conversation+if+you+want+to+clarify+a+point+or+add+to+the+conversation"&as_epq=&as_oq=&as_eq=&as_nlo=&as_nhi=&lr=&cr=&as_qdr=all&as_sitesearch=&as_occt=any&safe=images&as_filetype=&as_rights=

So that's the context in the example you've given. As for the other possible meanings your phrase might have, that depends on the context each time....

My apologies again if you disliked what I said, but hopefully you now have (above) all the information you need.

John

PS – Link: It may be that the link in my previous post won't open in Russia because it's a US military (although public) website. However, the same document has been copied to/from an EU website and a few other publicly-accessible websites. They're all listed in the new link I've given in para 3 above.