McLaren had targeted a May release for its first big upgrade batch for the MCL38 driven by Lando Norris and Oscar Piastri and has now confirmed that it is on course to bring the new spec to the Miami Grand Prix held on 5 May.
"For Miami, we will have finally the first round of upgrades to our car," team boss Stella confirmed in Shanghai.
McLaren has started off the 2024 season in promising form, nipping at the heels of Ferrari while having the measure of Mercedes so far.
But with the team realistic about needing perhaps another year of rolling development to really fight at the very front, Miami's upgrade package is the first of several steps in that direction.
In addition to adding pure performance, the update is also designed to improve how the car takes care of the tyres, with rear degradation a key differentiator at this weekend's Shanghai event.
"These upgrades will also include some attempts to improve tyre degradation, so we will try and see if we can take a step forward," Stella explained.
"Considering the amount of improvement we should do to get closer to some of our competitors, I would say that we need more than one round of upgrades in terms of helping the behaviour of the tyres.
"But for everything, this is kind of constant development. You never assume that that's good enough when it comes to keeping the tyres in the right operating window.
"Certainly the next one will be another interesting one from a tyre point of view.
"Especially if in Miami we have high temperatures like we had previously, so that track becomes quite a bit rear limited; a lot of traction with low-speed corners and then acceleration."
Norris and Piastri qualified fourth and fifth for Sunday's grand prix, after finishing sixth and seventh respectively in the 19-lap sprint.
Stella said it was clear that Red Bull and Ferrari still have a better handle on keeping the rear tyres alive, with front graining less of an issue than first thought by many.
"I think the track has actually been quite consistent in the fact that the main limitation is the overloading of the rear axle," he said.
"This is not a surprise because this track in terms of tarmac, despite the surprising coating, it's more on the Bahrain and Suzuka side.
"We know we become overloaded at the rear, which some cars cope better than us, for instance, Ferrari and Red Bull.
"In terms of front-end limitations, interestingly, I think since we introduced the wide tyre, there's been much less graining in China than what it was like before 2017."
