if I'm not mistaken, RBF can be done by adjusting output amount (decrease output and increase fee)
so I think you can't do RBF and send to another address at the same time
trying to send the same utxo to another address is called double spend attempt
RBF is essentially a double spend; your UTXO is double spent to initiate the RBF, whether if its to the same address or not. You can change your output to wherever you want or change the amount. What you're thinking is FSS-RBF which is not widely adopted but it was only adopted by F2Pool at one point before everyone switched to Opt-in RBF.
My Electrum experience, and assuming this works for all clients, RBF only increases the fee. Every other spend detail of the transaction is a copy of the original (receiving address, amount to be transferred, input address), except for the specified fee (and of course the tx ID itself), at least this is how all of my RBFs look like in Electrum. When I choose to RBF, only fee area is not grayed out.
Electrum would sometimes spend from another UTXO or decrease change amount if the fee is not sufficient.