Remember all housing loan rates are negotiable. You can always play off one lender against the others to some extent.
Once you have reached the limit of negotiation on interest rates you can then negotiate the other charges especially processing fees.
Unless loan amount is a constraint, approach prospective lenders only after the property is finalised and disbursement is required in the next few days. Most lenders are interested only in disbursements and reserve their best rates only for immediate disbursement cases.
Bundle your loan request with the loan requirements of your friends and colleagues and thus offer a larger loan portfolio to the Bank. This can be specially powerful if the property is in the same building since the legal and technical costs can be reduced which can then be passed on as a benefit to you.
If the property is being bought from a reputed builder, you can also employ the month end trick by negotiating till the 23rd or 24th of the month. Every Bank has monthly targets for its staff and as the month end nears the Bank offers slightly better terms to enable them to fulfil their target. However, this is unlikely to work where the property title / valuation is not absolutely clear.
Give full details about your existing borrowings (including credit cards) and good repayment track record to all lenders. Remember most banks will check with the Credit Bureau anyway to find out about your existing borrowing and repayment track record. So making full disclosure about your existuing borrowings makes sense and can actually be used to reduce rates further.