It is correct. "Company" is parallel to "my shoulders", which is reasonable.
It would be somewhat odd to say "the company's" as that would suggest "The company's shoulders", which is stretching the metaphor: do companies have shoulders?
If you want to avoid the parallelism, you could rephrase to something like:
It won't fall only on my shoulders, but ...
Ok, first of all, I should clarify that there are two forms of the verb here that are often confused:
"have gotten" -- This is the present perfect form of "get". It implies something has happened (but may be continuing to happen) at some (unspecified) point in the past.
"have got" -- This is an idiomatic (not grammatically correct but frequently used to ...
It's considered polite, and it's more commonly used in writing, to leave the first personal pronoun(s), such as I, and the possessive pronoun; mine, at the end.
My husband and I.
I and my husband.
Which is perfectly grammatical but no one says it.
Therefore, in the OP's situation it is preferable to say
Tessa's books and ...
The title and the question are different. I am answering the question.
It should be:
My books and Tessa's (books)
or you may say:
Tessa's books and mine.
becauseme is the objective case of I.
here we are talking about the possession of books.
So we have to use the possessive case of I- my or mine.
Different interpretation from the other answers:
Timisoara's public transport network: You are refering to the public transport network of Timisoara, as in Mathilda's car
Timisoara public transport network: You are refering to the name Timisoara public transport network.
Both would be correct.
What we are trying to say here is "The public transport network of Timisoara" / "The Timisoara public transport network". So, we can change "the" to "-'s" in this sentence and it would have the same meaning.
However, it is not uncommon to omit the "the" in titles, street signs, newspaper articles etc in order for it to be read faster. This is perfectly ...
In connected speech or text, it needs to be definite, so it needs either the possessive "Timișoara's public transport network" or the definite article "The Timișoara public transport network".
Titles, captions of diagrams etc, often use "headlinese", omitting articles and some function words; in that context forms like "Timișoara public transport network" ...