Sounds like you are describing the Tektronix TM500/TM5000 line, introduced in the early seventies. Hameg had (has?) the less ambitious HM8000 line. They had edge connectors that carried AC and DC power rails and some optional unused pins for interconnections between modules. They had power supplies, pulse/sine/function generators, DMMs, frequency counters, even oscilloscopes and some specialized gear like differential and current probe amplifiers. The motivation behind that was that transformers were expensive, and so were displays.
This way you could have say a function generator without a display, and if the user needed an accurate frequency read-out, they would add a frequency counter plug-in that would be internally connected to the function generator. If you wanted an accurate level read-out, you could add a DMM plugin to do the same. Ultimately these instruments required much more R&D than stand-alone because the power, EMC, thermal and size constraints they had to work against. Especially when cheap LCDs removed the cost advantage of sharing displays. Usability was also compromised due to the much more limited front panel real-estate.
Another application was building custom systems. You could use a function generator to drive the VCO input on another generator to sweep. This way you could generate complicated signals. These days, you just add another sweep generator inside the function generator, or use an arbitrary waveform generator. If you want a power supply that can output arbitrary waveforms, you just add an arbitrary waveform generator inside the power supply. Tektronix sold the TM5000 lines to Tegam in the late eighties, who put it on life support for a number of years before killing it.
These days, when you can find cheap AC-DC and DC-DC power supplies, and LCDs can be bought for a few $, I do not see the advantage. If you want something that looks nice together, build instruments in matching cases that stack well together, like you see on many half-rack Agilent/Keysight and Keithley instruments.