I think your best way forward is to talk to multiple banks, ask for their offers and compare them with each other.
Normally, some brokers will take care of the upfront stamp duty, etc. other costs from their commission that they get. However, you are more likely to get a much better rate if you talk to the banks directly & negotiate hard. The bank teams have room to lower rates and have further room to lower rates by taking approval of higher authorities.
Start with a target of the lowest rates generally being offered by any bank and see where you land. Hopefully, much lower than the existing rate.
Since you are looking for top up, on a total basis, you will probably be better off with existing lender even if interest from ICICI is higher than other banks by 0.1% - 0.25%, as it will help save you documentation time, costs, etc.
Please read the fine-print of the top up documentation carefully. Many people may tell you that it is OK and they'll manage all paperwork. However, you will be the one signing the documents so do read them once, as there will be lot of conditions that come attached with it.
Typically, 'home improvement' top-ups are given for furniture, white goods, etc. kind of improvements. They will ask you for some paperwork / invoice / quotation to say how much you plan to spend on such improvements.
The other type is LAP i.e. loan against property top up. These amounts generally have lesser restrictions.
