[clause] + ,不过 + [clause]
[subject] + 不过 + 是 + [noun]
不过 at the start of a clause adds a "but". It's softer than 但是: the second half qualifies the first rather than overturning it, so it fits a small complaint or a polite objection.
It's common in speech, and also fine in writing. 虽然 can open the first half, as it does with 但是.
As "but", 不过 comes first in its clause, before any subject. After the subject it means something else: "only", "merely", "no more than".
All three can mean "but". 但是 is the plain, neutral one and the right choice for a strong contrast. 可是 is spoken and can sound a little complaining. 不过 is the mildest.
Use one at a time: 但是不过 and 可是不过 are both wrong.