I don't see why not.
India is an example.
When I say Indian, you think of dark-skinned people
whose ethnicity is Indian.
However, Indian actually means people from India, like how
Singaporean means people from Singapore. But 'Singaporean' is not a
race right? So why is 'Indian' a race?
Indians are made up of many, many different ethnic groups. We
have Hindi, Punjabi, and 17 other less well known ones. But
somehow, collectively, they are known as Indians. Maybe, for this
reason, I don't see any racism among them.
So, why not Singapore?
There is always racism among the Indians themselves and in
neighbouring Nepal, Bangladesh and Sri Lanka.
http://www.boloji.com/wfs5/wfs677.htm
In the states of Nagaland, Manipur, Mizoram, Tripura and
Arunachal Pradesh, where the majority of the people there are
yellow skinned and have eyes with the epicanthal fold, they are
always rejected and laughed at by Indians from other areas
belonging to the Indo-Aryans and the Dravidians.
In the state of Maharashtra, where the Marathi form the
majority, have always been discriminating against the Bhojpuri
people and accusing them of being "dirty".
http://www.bdnews24.com/details.php?id=169714&cid=2
http://www.newagebd.com/2010/jul/14/edit.html
In the state of Orissa, West Bengal, Jharkhand and Bangladesh,
where the Eastern Indo-Aryans reside, discrimination against the
Munda and Santal escalates from "name callings" to "people do not
even want to come close" to "attacks".
In Sri Lanka, Sinhalas discriminate the Tamils.
In Nepal, the Bahuns and Chhetris discriminate all the non-Bahun
and non-Chhetri, with the Newaris being the only non-Bahun-Chhetri
group coming out as the most successful group which is being
discriminated against.