Select only some variables to base my analysis (without losing the other)

Hi everyone,
I need a little help with my analysis: right now my dataset is something like this

Age Gender V1 V2 C1 C2 F1 F2
20      2      1  1  2     4
23      2   1     4  3   
21      1   3  2  2     3

The most important of my variable is V# and I want to base my deleting NA process from it to create a new dataset where I will fill the missing data with mice.
My problem is that I don't know a way to select and work only with V# values without losing all the other information. In fact, I tried using select() but when I save my file I've only the V variables and nothing else.
For example, right now I need to say to r "basing only on V variables delete all row that have more then 5 missing values but keep Age, gender, C and F" and so on.
Thank you so much for your help

here I filter the iris dataset based on variables with name beginning Petal of which there are two, and I filter out all records that dont have a value over 6 in those.

iris %>% filter_at( vars(starts_with("Petal")),
                    any_vars(.>6))

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Hi, thank you for your answer, I've tried using your code but it gives me back only the name variables without the data. Is there something like select() or a way to to only temporary select some variable to work with without losing the other or just added them back (edited) later?
Thank you again