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I was at the trade show and came across (with) the boot of your company...

... is this "with" needed or not in this phrasal verb? its meaning is "found by accident" isn't it?
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Hello V.

There seem to be 3 possibilities where 'come across with' is used as a block:

(1) 'To come across with [something]' = 'to provide [something] that is expected', e.g.

'Eventually Jojo came across with the $300 he owed me.'
(i.e. 'Jojo paid up'.)

(2) 'To come across' + 'with' = 'to come over to see' + 'with', e.g.

'Eventually Jojo came across with the $300.'
(i.e. 'Jojo crossed the room with the $300'.)

(3) 'To come across' + 'with' = 'to communicate' + 'with', e.g.

'At the concert, the trumpets came across with surprising resonance'.

Possibilities 1 and 2 seem most likely, unless (as you say) it was simply a mistake for 'come across' = 'encounter by chance'.

On the other hand, the phrase 'the boot of your company' is a little strange. Is this a translation? Or would more context be available?

MrP
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I think your guess is right, but I'm not sure. The meaning is undoubtedly correct.
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 MrPedantic's reply was promoted to an answer.
it's a typo, booth sounds better?

... so as per the above answers and to become absolutely clear let me recap:

"I was at the trade show and came across with the booth of your company" ("with" needed)

=

"I was at the trade show and found by accident (encountered by chance) the booth of your company"

correct?
Hello V.

I would say, yes, 'encountered by chance', unless the booth in question was unusually portable.

The 'with' sounds like an accidental interpolation, to my ears. But it's possible that it's used in some lavishly prepositional variety of English somewhere else in the world.

'To come across' is an interesting verb, because it's often used in contexts where the element of chance is in fact minimal:

'Oh, by the way, I came across this in your intray last night...'

Which means:

'Oh, by the way, after you'd gone home last night, I went to your desk with the express intention of finding that invoice you claimed never to have seen, and after thoroughly searching through all your drawers and papers - would you believe it! - I found it in your intray...'

(Not that I'm bitter about that invoice.)

MrP
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I checked the dictionary. It says come across sb/sth, so there should be no "with" after "across".