According to http://bloodborne.wiki.fextralife.com/New+Game+Plus a user (ublug) has found that blood echo drops from bosses scale according to the following:
ng++ = 10% more than ng+
ng+3 = 25% more than ng+
ng+4 = 50% more than ng+
ng+5 = 100% more than ng+
ng+6 = 150% more than ng+
I was unable to find any other quantitative evidence about scaling between the levels.
One may try to extrapolate from this data that enemies will be 10% harder to kill and will deal 10% more damage on ng++ compared to ng+. A similar approach could be taken by estimating boss health at each level of ng+ to estimate the scaling, but this does not seem entirely correct.
If we look at the design of Dark Souls 1, we see the following http://darksouls.wikidot.com/new-game-plus
A single formula cannot be applied to the increase in enemy HP and
Souls between NG and NG+. This is because they increase by
inconsistent amounts, usually corresponding to the location. In NG+,
enemy HP is usually between roughly 1.5x to 2.5x of NG values, while
souls dropped are usually between 2x to 5x NG values. There are
There is likely a similar system in place for Bloodborne.
Dark Souls 1 also featured a cap in difficulty upon restarting:
After the seventh playthrough is completed, the game will no longer
increase in difficulty after it restarts. NG+7 and any subsequent
playthroughs are a repeat of NG+6. It is a common misconception that
NG+7 is the highest difficulty.
The same cap existed in Dark Souls 2.