What subwoofers keep up with Quad ESL 57 ?

REL B3 would work.

I use a pair of TBI subs which work nicely with Quad 989s

The room is the dominant factor at bass frequencies. Not to say that different subs don't sound different, but the peak-and-dip pattern imposed by the room is quite audible, as is the progressive boundary reinforcement ("room gain") at low frequencies that makes a "flat anechoic" sub sound boomy and slow, and a sub that rolls off high and gradually sound tight and fast. The ear actually has very poor time-domain resolution at low frequencies, so the subjective impression of "slowness" is really a frequency response issue; in studies where group delay was digitally separated from frequency response, group delay proved to be barely audible on test tones and inaudible on music. On the other hand, frequency response anomalies were readiliy audible if they spanned a large enough portion of the spectrum (which happens routinely in the bass region).

Dipoles have been shown to have smoother in-room bass than monopoles, so this makes matching a pair of dipole main speakers with a single monopole sub often frustrating. The ear can often hear the discrepancy between the smooth upper bass of the pair of dipoles in contrast with the lumpy middle and lower bass from the sub. Using two subs helps a great deal, as each sub will interact with the room's bass modes differently, and the two dissimilar peak-and-dip patterns will smoothe one another out. I advocate taking that one step further and using four small subs... preferrably, small subs that are tuned to take room gain into account.

I know it seems highly counter-intuitive to use a lot of subs when your goal is quality instead of quantity, but this is the best way to get the room to work with you instead of against you. And the elephant in the room is... the room. The multisub approach is effective at extending the smoothness inherent in a good dipole like the Quad 57 down into the low bass region.

Imo, ime, ymmv, etc.

Duke
dealer/manufacturer

The REL would be my choice.

I would buy the small Definitive Technology Supercube III, great little sub, you can connect it via the speaker terminal off your amp, or many other and multiple ways.

Very, very fast and deep little sub.