I guess the key point of your question is "list on more than one exchange", if my understanding is correct. I have following thoughts for your reference:
1) reputation: if a company want to enter into a market (to sell its products/services) of that particular country, it needs to build trust in the business community and among customers, to get listed in that country's stock market can help that;
2) access to funds in that particular country/currency: sometimes, the company (e.g. already listed in the US) may need a currency, e.g. euro, for business reasons, it may choose to list in an european exchange.
3) pricing: e.g. if a company needs to raise a lot of funds in its IPO, investors in one stock exchange may not have the appetite to accomodate such size of offering, to raise funds from more than one exchange is a better choice to achieve good pricing.
There may be more reasons that are beyond my knowledge.
Hope the above can help you a bit.