You need to count how many different days that you will board a train. 

I suggest that you start by looking at how long time the train takes between the cities you plan to visit. https://www.bahn.com/en is a good place to start.

If you are planning to use night train and high speed trains (not in Germany) you need to make reservations and those might sell out.

You’d like to go:

1. Stockholm to Amsterdam
2. Amsterdam to Paris
3. Paris to Nice
4. Nice to Milano
5. Milano to Stockholm

You are asking if these five (!) segments are possible to do within four (!) travel days? 

Next:

Is it possible to go from Stockholm to Amsterdam in just one day on a sunday? I think it’s a good idea to use a timetable (as mentioned before).

Is it possible to go from Milano to Stockholm in just one day? I think it’s a good idea to use a timetable (as mentioned before). At least this is possible with just one travel day when using a night train to Stockholm (but you’d need to travel one day later). 

Example

Stockholm Sunday the 12th 16:12

arriving in Amsterdam monday 13th 11:00…

would that count as 1 day?

You need to count on how many different days that you will board a train. 

I suggest that you start by looking at how long time the train takes between the cities you plan to visit. https://www.bahn.com/en is a good place to start.

If you are planning to use night train and high speed trains (not in Germany) you need to make reservations and those might sell out.

 

Example

 

 

Three days.

 

Three days.

 

Two days from Milano.

Two days.

A travel day is from 00.00 CET to 23.59 CET. A quick count I made gives that you need 7 days.

1. Stockholm to Amsterdam 2 Travel days
2. Amsterdam to Paris          1 Travel day
3. Paris to Nice                     1 Travel day
4. Nice to Milano                   1 Travel day
5. Milano to Stockholm         2 Travel days

So true.

@yasminejak But if you’d leave from Milano one day later, it’d be possible with just six travel days. ;-)

But there’s no pass for this...

Are you taking the night train, Snälltåget, from Hamburg to Stockholm then? That's the only way that you might get from Milan to Stockholm in one travel day as the night train counts as one travel day as long as you don't board another train on the arrival day of the night train.

There are seats available on Snälltåget on the 23rd and 25th, not on the 24th.

It’s just running to Malmö the 24th.

Ok. Due to railworks I presume. I will go with Snälltåget in July and August and I had to adopt the travel schedule to the railworks.

Going only to Malmö with Snälltåget would then mean an extra travel day to get to Stockholm.