Originally Posted by
B747-437B
India does the same if you request. They don't advertise it, but it is possible.
Rule 13 of the passport rules, 1980 even has a section on it:
13. Issue of additional passport or travel document in special circumstances.-A person holding a passport or travel document shall not be entitled to another passport or travel document unless he surrenders to the passport authority the passport or travel document already held by him:
Provided that separate passports or travel documents may be issued to the same person in respect of different countries if it is necessary to do so to facilitating his visits to such countries.