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For consulting and processing business, today, in India, there is only one company which offers world-class software solution with outstanding support and economical rates. It is greytHR https://www.greythr.com/customers/
All your requirements are met except one "desktop version." greytHR is a cloud-driven solution which run on a browser (Help you save the additional investment on servers and related infrastructure).
I would recommend you to try for a few customers, experience the feel and I am quite sure you will join the list of hundreds of processing partners of greytHR.
From India, Bangalore