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Here's the sentence:

I don't see him very much now

Every rule says that time expresions like "now" (which actually stand for "these days" in this sentence, in my opinion) are used with the Present Continuous and not the Present Simple...

thanks in advance,

ps. and one more thing:

Could I say I spend more time with my girlfriend these days ? instead of I'm spending... ? I mean... I know that these days is used with the Present Continuous, but doesn't it imply here that I spend more time with my girl every time I go out with her? I mean... as a routine?
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Every rule says that time expresions like "now" ... are used with the Present Continuous and not the Present Simple...
That doesn't sound right. now with the simple present is quite possible.

Could I say I spend more time with my girlfriend these days ? instead of I'm spending... ? I mean... I know that these days is used with the Present Continuous, but doesn't it imply here that I spend more time with my girl every time I go out with her? I mean... as a routine?
No. It doesn't imply that. You spend more time with her in total. It could be one hour five times a week or five hours once a week. Neither tense says which.

All of these have the same basic meaning:

I spend more time with my girlfriend these days.
I'm spending more time with my girlfriend these days.
I've been spending more time with my girlfriend these days.


CJ
Comments  
«Every rule says that time expresions like "now" (which actually stand for "these days" in this sentence, in my opinion) are used with the Present Continuous and not the Present Simple...»

It is a bad rule that is superficial, that is, not reflecting the nature of things. It is just mnemonic rule, a rule of thumb. Yes, in many cases Now (meaning NOW) used with Present Perfect. But it's wrong about "these days".

The action in question is episodical. And it is present. So it requires Present Simple. The structure of "seeing" in your question is just the same as that of "going" in:

"I go to school every day"
"I go to school three times a week these days."
"I don't see him very much these days"
"I don't see him very much now"

The last two sentences have absolutely the same meaning, so there is no reason to use different tenses in them.
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 CalifJim's reply was promoted to an answer.
so... what actually am I supposed to choose, when the book gives me two options and I have to pick just one of them, like in this one:

"I spend/am spending more time with my girlfriend these days" - this is taken from a book... which one to choose?

thanks
In this case I prefer "I am spending more time with my girlfriend these days".

Though I am not sure whether the Present Simple version is ok or not...
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Forum_mailso... what actually am I supposed to choose, when the book gives me two options and I have to pick just one of them, like in this one:

"I spend/am spending more time with my girlfriend these days" - this is taken from a book... which one to choose?

thanks
I would choose 'I am spending' in this case. If we expanded this sentence a bit, we might get something like this:
' I don't usually spend too much time with my girlfriend, but I'm spending more time with her these days. ' (think of the second part as the exception to the rule)

And don't rely on the time expresions, it is sooo wrong! Look at this:
Did you have lunch today?
I had a meeting today.
You can use 'today' with the past tense, but you can use it with many other verb forms as well.