Is it possible to use a single domain for multiple mail servers that are located geographically in different countries?

Let me explain our current scenario.

Our company has 3 offices in different countries .
All these offices are using separate mail servers with more than 1000 users

Country A
Mail server: company.net
Users: a1@company.net, a2@company.net, a3@company.net ..

Country B
Mail server : company.org
Users:b1@company.org,b2@company.org, b3@company.org.....

Country C
Mail server : company.biz
Users: c1@company.biz, c2@company.biz, c3@company.biz...

What we require now is to put all these users under a single domain name , company.com
How can we use one single domain for all these different mail servers?
We wish to have separate in house mail servers at each country so that the local mails can be locally delivered.

What we have to do for this? Please give a solution....!