. What can we offer rose if we resign Fournier as well
It is not as simple as this. The simple answer is that whether we sign Fournier or not, we are over the cap and cannot sign any FAs, Rose or otherwise, unless we use the MLE or do a sign and trade.
If you want to do a sign and trade, you could send out as much salary as you want. For example, if we send out Smart and Thompson, you could sign Rose for $20M or even more and still have some money to sign Fournier (but not much else due to the hard cap that would apply).
If you don't do a sign and trade, the only option is to use one of two version of the MLE. The non-taxpayer version of this is $9.2M but his would hard cap us and with no other salary going out, would only leave us $5M or so to sign Fournier. The more realistic version is the taxpayer version that is $5.7M. If we stay under this value, we can sign Fournier for whatever we want albeit we will be subject to tax.
So the long, convoluted version of this is that I don't think it is worth getting hard capped for Rose so the practical limit to this is a max offer of $5.7M (the full taxpayer MLE). In order for a S&T to result in enough "room" (under the hard cap) to sign Fournier, NYK would need to back more salary than Rose is signed for. NYK is under the cap so they could in theory accept Thompson ($9.7M) and say Grant Williams ($2.6M) and if Rose took maybe $8M, that would free up enough for us to sign Fournier and stay under the imposed hard cap. I don't see this as very likely.