No, don't use multiple ground points.
What you want to look at is study the isolated ground / dedicated ground techniques used in every modern hospital, serious R&D labs near wafer fabs, and anywhere high precision measurements are done, and you need to keep your measures low noise even though there might be heavy, noisy current flows on the building power mains cables.
Think of the "IG" (Isolated Ground) or DG" setup (dedicated ground which is similar except uses a relatively large ground conductor compared to what is normally called for) as a Star Ground connection system where you have a very good single ground connection to Earth, and that is a common Earth bond point between your lab, utility power source and mains distribution protection system. When I say a "dedicated lab ground" that is essence a larger, very low impedance cable leading from your test area back to the very good common bonded ground point outside of the lab room - for instance where you have -multiple- ground rods installed for the mains power system entering the building.
The concept here is that for sensitive equipment you're NOT using the relatively high impedance, noise-coupled copper wire that runs along side the mains cables to make your ground connection - with a DG you're using a good heavy conductor that takes it's own low noise path to the COMMON very low resistance ground point....and you DON'T want to run that ground DG cable along side the normal high-noise mains wiring.
You can still have a common ground bus bar on the test bench like you have but that would be connected to your isolated / dedicated ground conductor (ALONG WITH YOUR "IG" rated equipment sockets) - which is the good heavy conductor that does NOT run along side the power cables. You are still safely connecting back to the bonded utility ground point - just in a low-noise way.
On some systems where shielded isolation transformers are used, the transformer primary section uses the standard utility ground wire on the power plug, but the inter-winding shield and secondary side uses the isolated & dedicated low impedance ground system.
Generally (as required by law for certain commercial buildings) there is also a grounds circuit monitor system in place that will instantly trip off the mains power (or sound an alarm) in case a safety grounding system goes open for some reason.
You never want to create a "floating" ground situation - that is where you have a ground system that is completely disconnected from the utility / power source ground. That creates a situation where if you have an equipment failure where a utility mains "hot" circuit can energize the outer cabinet of a piece of equipment - and the mains circuit breaker or GFCI never trips...that's bad. Don't ever let that happen. You always need to look at your setup and guarantee that the basic testing setup poses no danger to the equipment operator. If there is a human contact hazard by the nature of the setup, then that situation needs to be clearly labeled, and perhaps lockouts, safety interlock switches on cabinets and/ or requirement that Personal Protection Gear be worn. At least here in the States that is usually a strict issue with insurance companies and the annual fire / safety code inspectors.
It just depends on the safety / grounding situation and what voltage / energy levels you're looking at. Usually we never even think about this when testing low voltage, low power circuits < 50VDC - but when you start taking precision measurements at higher voltages - it doesn't take more than one hard accidental "bite" to realize you need to keep your grounding system safe and low-noise.
EDIT: In the final analysis: Your most sensitive gear on the lab bench would either get power from isolation transformer or plug directly into IG type mains sockets, and those IG's are grounded to your heavy bench ground bus bar and low impedance DG cable, which in turn runs back to the common utility-bonded grounding point. That makes everything on your test bench sitting at -one- single common reference point.
Your lab lighting loads, outlet boxes, conduits and mains raceways, motors etc. would still be grounded the standard way.
NOTE: You will see some info on the 'net talking about how "IG" systems sometimes don't work well, usually written by non-metrologists who don't normally measure down in low ppm - but the difference here is that on high performance systems you're using a very high performance, heavy grounding conductors - not the piddly little noisy mains wire electricians refer to as the "ground wire". If you're chasing ppm, you want a test bench system ground setup that has much lower noise & impedance ground than you'd find in a typical wiring setup.