The short answer is no. Viruses are incapable of replicating without a host cell. So even if virus A bound to virus B, it could not infect virus B.

But I think what you are asking is actually a question about super-infection - can a cell be infected with two viruses? That answer is a resounding yes. Super-infection is well known in virology - it is how influenza viruses diversify.

So if you could engineer virus A to inhibit the replication of virus B, and then super-infect cells infected with virus B, would it staunch the virus B infection?

That, sir, is a very interesting question. I do not know that it has been attempted.

YES.

They are called Virophages. One example is Sputnik which infects mimivirus

Take a look at this paper:

https://www.nature.com/articles/nature07218

And the article

https://www.nationalgeographic.com/science/article/the-virophage-a-virus-that-infects-other-viruses?loggedin=true

Thank you so much Gary Lee Gilmore for your interesting replay

Thank you so much Mohamed A. Eltanbouly for your wonderful answer.

Yes, in specific conditions.

Thank you Aalae Salman Ayit for your replay

I stand corrected! I was unaware of virophage. Thank you for the enlightenment, Mohamed A. Eltanbouly

Falah Hasan Obayes Al-Khikani

Please go through the following RG links.

Article Virophages of Giant Viruses: An Update at Eleven

Article Viva lavidaviruses! Five features of virophages that parasit...

Thanks!

Thank you so much Arvind Singh for replay.

Yes it is

Good question

I thing yes

Interesting discussion

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following

Temojeen F Kh, thanks

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Thank you for adding your reply. temojeen

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Thank you for adding your reply. Kadem

Thank you for adding your reply. Pa

Yes

Thank you @Rajesh A M