New Williams team boss James Vowles has passionately sought to give the team a way to catch up on its ageing Grove base's facilities.
Under F1's financial rules teams have a $36 million allowance over a four-year period to invest in capital expenditure, with an exception made for wind tunnels.
But according to Vowles that figure is nowhere near enough if Williams is to catch up with F1's top teams.
However, talks to find a solution have not produced any results yet, with rival teams keen to secure bigger CapEx allowances for themselves as well if any concessions are to be made to Williams.
"Some teams jumped on that bandwagon to say, but actually, we would like to have a little bit more CapEx," Mercedes chief Toto Wolff described the discussions.
McLaren's Brown says he is "sympathetic" to Williams' situation, but warned that any solution for the team cannot ignite another free-for-all spending spree.
"I am not a fan of bigger allowances, just in general. I'm sympathetic and cooperative on Williams having the chance to catch up," Brown told Autosport's sister website Motorsport-Total.
"The problem is, once that got presented, all the other teams jumped in who then wanted to capitalise and go: 'Well, I want something'.
"What started off as a Williams request to catch up turned into a conversation of should we all get 70 to 90 million?"
Brown reckons a singular solution for Williams will be hard to drum up support for, as rival midfield teams will then simply argue that Williams will not only have been able to catch but even overtake them with newer facilities.
"The problem is if Williams gets caught up, then some teams are going to go: 'Yeah, but their stuff is newer than mine, so I want to be caught up'.
"So, I don't know how we get there. I'm sympathetic to Williams' situation, I'm supportive of it, but not if it just opens up a spending spree. And that's what started to happen.
"What started off as 'let's help out Williams' turned into half the teams wanted more money. Half the teams didn't.
"I'm fundamentally against more money being spent just because we've all got more resources. It'll just create a spending war again.
He jokingly added: "I think the whole reason why the sport is so competitive right now, other than Max [Verstappen], is [the budget cap] is working.
"If you took Max out of it, you'd have had 5 or 6 teams that have already won. We need to put a budget cap on Max's right foot!"
