I am a HiFi-fan since I was 14 years old. I had a lot of different gear, and the possibility to take some stuff home over the weekend from a local HiFi-dealer where I jobbed.

Topping D70S DAC for the main system
Topping E30 DAC for the computer
foobar player
Pro-Ject Stream Box DS
Linea Research ASC 48 FIR digital speaker management system modified with OPA1612 ultralow noise, ultralow distortion, high slew rate operational amplifiers
1 x Crown XLS 1502 stereo subwoofer amp
active Neumann KH 310 A near to mid-field studio monitors
2 RiPol subwoofers with chassis measured and matched by Axel Ridthaler (4 Gladen RS 15 free air, 2 each in parallel) [29 Hz -3 dB]
for the computer: Adam Audio T5V active nearflied monitor with Adam Audio T10S subwoofer

some previous components:

Tang Band W8-1808 / Eminence Alpha 15A open baffle dipole speakers [40 Hz -3 dB] with 6 x Hypex NCore 400 mono amplifiers
Acapella Ion TW 1S plasma tweeter [in German: Ionenhochtöner]
Corona plasma tweeter
Capaciti Element 160 electrostatic full-range speakers
QUAD ESL-57 electrostatic full-range speakers
Apogee Centaurus Slant 8 magnetostatic hybrid speakers
Magnepan SMGa 2-way full-range magnetostatic speakers
Tannoy Little Red Monitor
Yamaha NS 1000 Monitor
ESS AMT 1 Oscar Heil Air Motion Transformer, Lowther PM2A
RiPol subwoofers (Peerless SLX-315 12 inch) with active crossover Ridtahler RMS Audio SX-1 Linkwitz-Riley 24 dB / Oct
Revel Performa B15 active subwoofer

Pass Labs X 150.5 power amplifier
Spectral Megahertz DMA-100 S, DMA-80, DMA-50 power amplifiers (all Spectral are the finest amps, but not so much the 80)
Spectral DMC-20, DMC-12 preamplifiers
Audionet AMP II MAX dual mono power amplifiers
Accuphase E-303X, E-205 integrated amplifiers
Hypex DLCP Digital Loudspeaker Correction Platform
Wyred 4 Sound DAC-2
AFW 1 active crossover by Ralph Stens
Wadia 860x and 830 CD-Players
Shanling CD-T 100 tube CD-player

Stax Omega II with SRM-007 t amplifier, SR Lambda Signature with tube amp SRM-006 t

Artisan Silver Dream pure silver cables, Monster Cable Sigma Retro Gold RCA interconnects and speaker cables, Fadel Art "The Stream Duo" speaker cables, "The Pro Line" interconnects, Nordost Heimdall RCA interconnects,  Audioquest Yukon and Columbia, Kimber 8 TC speaker cables, Kimber Timbre cables

Yamaha C-2a, Yamaha C2-x preamplifiers, Kenwood L-08M high speed dual mono power amplifiers, QUAD 606 MK II, 405-2 (op-amp modified), Sony CDP-XA 30 ES, Sony CDP-557 ESD, analog players with SME arms, moving coil pickups Dynavector Karat 23 Ruby, Yamaha MC-1000, ... ... ...

Modification Area:

The most devices in the mid range to entry level high end use ICīs somewhere in their circuitry. There are standard types in use for the analog audio sections in the input stages of amplifiers or analog output stages of digital devices. In some cases you will find a NE 5534 (single channel) or NE 5532 (dual channel). There are older ones, like TL-071 or LF-356, and so on. The NE 5534 are standard types even in studio/professional equipment. The quality of this IC limits the overall quality, no matter how good the rest of the circuits might be. There are some types of very superior quality, made by manufacturers like Burr-Brown, Analog Devices, Ultra Analog, Precision Monolithics, ... I started with some OPA-37 AZ a few years ago, and they were very much better in sound. Today, Burr-Brown manufactures the OPA 604 (single channel) and OPA 2604 (dual channel) especially for audio equipment, and the newer types OPA 134 / 2134. They cost only a few Dollars each. They are pin to pin compatible with the older ones you want to replace. You just can solder the old ones out, and the new ones in. More expensive and superior is the OPA 627 and OPA 637 (which is not unity gain stable and needs an amplification of at least 5). Recently I switched to Analog Devices LME 49710. The AD 847 is not bad, but it had DC offset in several applications.

I will give you no quarantee, for any modification, but I will show you which ICīs you can replace with better types: 

old type Burr-Brown type direct replacement possible
LF 356 OPA 602 (single) depending on circumstances
LF 357 OPA 637 (single) depending on circumstances
LF 412 OPA 2111 yes
AD 712 OPA 2107 depending on circumstances
LM 358 OPA 2111 depending on circumstances
TL 081 OPA 604 (single) yes
TL 082 OPA 2604 / LME 49720 (dual) yes
NE 5532 OPA 2604 / LME 49720 (dual) yes
NE 5534 OPA 604 (single) yes
NE 5534 / OPA 604 / OPA 627 / 637 / 27 / 37 / 132 / 134, ... LME 49710 (single) yes
TL 071 OPA 604, OPA 134, LME 49710 (single), OPA 1611 depending on circumstances
TL 072 OPA 2604, OPA 2134, LME 49710 (single), OPA 1611 depending on circumstances
NJM 4560 D OPA 2604, OPA 2134, LME 49720 (dual), OPA 1612 depending on circumstances
OP 275 GP OPA 2604, OPA 2134,  LME 49720 (dual), OPA 1612 depending on circumstances
other types for OPA 604 OPA 627 / 637 / 27 / 37 / 132 / 134,  LME 49710 (single), OPA 1611 depending on circumstances

The most preferable type is the OPA 1611/1612 and LME 49710/LME 49720. The circumstances, which have to be taken into account are aditional circuitery like offset-nulling or drift-nulling, which are not required in most cases, and they might not be compatible. If you have "naked" ICīs, you most probably can switch over. Take care of rail voltage and the gain. Some devices have +/- 18 V, some more. Some ICs go only up to 18 V, others up to 30. Some are not unity gain stable - but should be in the circuit of interest. Some applications might be critical, like HF-signals in the digital parts of your CD / DAT devices.  But in the analog input / output stages of amps or pre-amps it is less critical. In some cases the limited bandwidth of slow ICīs prevents the amps from deadly HF swinging. With these new high-speed ICīs without limiting in another area of the amp it can result in lethal breakdown - also for the rest of the chain after this device! In any case, these are tips regarding the sound quality, but no recipies for general cases. Itīs better to ask a technician or service station. It is not advisable to modify here with the first time a soldering iron in hand, or with no idea in which part of the circuitery you are - and whatīs happening there. 

Also, you might want to refer to the manufacturer, Burr Brown, which belongs now to Texas Instruments.
In the case of a QUAD 405 and 405-2, you may replace the TL-071 CP directly with a OPA 604 or LME 49710 or OPA 134. It works fine. Not in the QUAD 606! This OP amp is not in the signal path but for DC offset regulation. Do not change it!

Construction part