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Not sure as to other banks. I have Bradesco. (It bought HSBC, which I have in the US.)
Bradesco charges around R$ 14,00 per $1,000.00 U$D transferred  via wire.
It is my understanding ITAU is a little more relaxed as to CC and loans, but again not certain.
If on SSA, you can have monthly deposits into approved BR banks. (I would not recommend all go to BR, you can have 1/2 to BR and other to your US bank).
All depends on your US bank as to fees on wire transfers.  Some Credit Unions have no fee or lesser fees on wire transfers.
FInd one of the major banks in Victoria and discuss with a manager (back office) if face to face is available.
Once you establish a working relationship with a bank, you will find it more pleasant, than just ATM's.
Once I established a relationship with Bradesco, I was able to increase transfers into the bank and, exceed the "standard" amount of withdrawal at the bank or its ATMs
Do some research. It is worth it.

I see your profile as Indian, so you must have an Indian bank account. But you must have a VISA prepaid reloadable debit cards under that flagship issued by your bank. I can withdraw more than R$30,000 in 2 days with 5 reloadable debit cards. You can reload as often as you want  depending on your needs. There´s a 1% foreign transaction fee on it. It´s funded by a credit card issued by the same bank. Just pay the monthly balance to avoid additional fees. Very convenient if you want extra cash in your pocket!

robal

Texanbrazil, thank you for your reply. I did go and have a word with the folks at ITAU out here in the City. Couldn't do the same with Bradesco since they have been closed due to the whole COVID-19 situation. Let's see, am still doing a bit of research and will finalize on something soon. Once again, thank you for your reply.

Thank you for your reply Robal, that's something interesting, the limit I mean. Will take a look into that.

You´re welcome and come back anytime.

You are welcome. I understand many banks are not "face to face" in many cities.

For relatively small monthly amounts just use Transferwise. There's no need to change your bank - Itau is fine for just keeping a running bank account in Brazil.
But for câmbio operations, learn how to use Transferwise - it's the easiest, cheapest, and fastest way to send small amounts of USDBRL back n forth.

There are other services as well. Transferwise is solid especially for Euros. Yanks have other options including a service now owned by PayPal.

There's no difference in how solid it is across different currencies - i.e.: it's as solid for EUR as it is for USD, GBP, CAD, etc. Please don't come on here and make silly statements like that.

As for other services out there - they're all carbon copies of Transferwise. Nothing earth shattering - simply choose which one works best for you.

"Please don't come on here and make silly statements like that."

It is not a silly statement IMO. If you are aware of Brasil's banking regulations, you will find the Gov., certain banks, and other issues are very different than other countries.
In recent days the MJ and PF have issued a "declaration" to enforce money laundering. Many banks, Cambios, and travel agencies have been shut down due to "suspicious" transfers. Some here have had a "hold" placed on their funds.

"Silly".

Interesting comment. Be well.