Takstar Pro 82's with fully open vents are already VERY bassy by most standards.
In my opinion it sounds best with 1 vent open anyway, since the bass just gets muddy when all vents are open.
The only headphones I can think of that is bassier than the Pro 82 and that are within your budget are the Meze 99 Classic or Meze 99 Neo.
Both still have 'bloated' bass like the Pro 82, but it's somewhat more controlled and tasteful.... they also have more mid-bass than Pro82, so they can sound a bit congested depending on what music you're listening too... so timbre is thicker and warmer than Pro82.
- To put that into numbers, Takstar midbass starts rising below 300hz, Meze 99 midbass starts rising earlier below 400hz.
If you're OK with about the same amount of bass as the Pro 82, but you'd prefer a DEFINITE improvement in EVERY aspect of the sound, then instead save up and spend a little bit over budget on a Beyerdynamic DT1770 Pro.
They're more detailed than Pro82, have much bigger soundstage and more linear midrange tuning.
They do have a bit more treble than the Pro82 though, but some of the juiciest, most textured subbass you can hear at almost any price point.... until you start spending more on closed-back biocellulose driver headphones.... and then it's more about 'flavour' differences anyway, not so much quality/quantity of bass.
