Extract lines that have two or more dots

\. and [.] are equivalent — they both match a literal dot, and not any other character. As a matter of style, pick one and use it consistently.
Your problem is that your regular expression (i.e., pattern) has ([^.]+\.)+ followed by [.]+. That’s really (sort of) equivalent to [^.]+\. followed by [.], with the result that your grep is looking for lines that contain text.text.., i.e., two dots in a row. If you check, you’ll see that your command matches a.b...
OK, I believe that the fix is fairly simple:
```
grep -P '^[^.]+\.([^.]+\.)+[^.]*$'
```
I.e., change the [.] to [^.] (perhaps that’s what you meant originally?), change the following + to an *, and add a $. After some number of text. groups, require/allow any number (zero or more) characters other than dot, up to the end of the line.
An even simpler approach (easier to understand) would be
```
grep -P '^[^.]+\..*\.' file.txt | grep -v '\.\.'
```
The first grep finds lines that begin with a non-dot character and include at least two dots. The second grep removes lines that have two consecutive dots.
Rather than do grep … | wc -l, just do grep -c ….

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