FWIW all teams have a system otherwise why have a coaching staff at all.
That being said it is my observation that BB's system is perhaps the most fluid system in the NFL. The BB system is not dictated by scheme but rather by Personal. Which means the players who make the team out of training camp will dictate the plays and schemes on both sides of the ball from week to week.
The only other team who comes close to this is the Cardinals with Bruce Arians. I have not watched the Cardinals enough to know if Arians applies this concept in week to week contests like the Pats or only in setting the overall strategy of the team each year.
At the NFL level every player has a lot of talent along with strengths and weaknesses. Most teams attempt to find players who will fit their scheme. BB looks at the players strengths and weaknesses and attempts to fit the players strengths to a scheme he can employ that will maximize the players success.
This approach is why even though the NE Coach and Gm have never changed during Brady's tenure here the team and its schemes have changed on both sides of the ball dramatically over the years.
This is why most players who have left NE have not seen a lot of success elsewhere. BB doesn't use a set team scheme in which individual players must fit rather BB schemes individual players strengths weaving them together with other individual team members to create a total team whose sum is greater than the individual parts that make it up.
In essence what BB does creates a force multiplier by weaving each team members individuals strengths into the whole.
Sadly this is, i believe a unique skill that BB alone possess, which when BB steps away from the game will never be duplicated again.
BB is truly a Giant among his NFL peers.