These COTO relays probably are custom specific, as this family still exists, but not with these part numbers.
http://cotorelay.com/wp-content/uploads/2014/09/3500_series_reed_relay_datasheet.pdfIn the 3458A-BOM, K1 and K3 are designated as 1µV relays, K4 is a 5µV relays, i.e. these are low e.m.f. relays, but have about 200V switching / breaking capacity only, if you compare the actual 3500 family datasheet, type 3501. Therefore, K7 is probably capable of switching > 1000V, and so to protect K1. It's COTO 5000-0124, probably a custom specific part.
Actual model may be COTO 5503, which has 3500V switching capability, and its case looks similar, see picture:
http://cotorelay.com/product/5500-series-high-voltage-reed-relays/So K7 is used to protect switching of K1, and for the 100V / 1kV range via K4.
Have a closer look at the switching of the low e.m.f relays K1, K3 and K4. These are probably nominal 12V types, and turn on at 9V already, following the actual datasheet.
All three are switched on by Q1 /CR1 with about 10V, but CR7 provides another ~4.5V hold level. This dual level provides power reduction (to 25%) to further reduce e.m.f. generation.
K1 and K7 have another special purpose, to protect the "Low Voltage DC Input" very quickly. (Also the other multiplexer- inputs in different DMM modes)
Both relays were controlled by dual FF U22, under normal conditions by the CPU.
In case of overvoltage on DCV, over R17/R19 at greater an input voltage than +/-14V, OpAmp U10A will quickly HW-reset K1 and K7.
R17 and R19 are 10k in total only, so 1000V overvoltage gives 100W, which must be switched off within < msecs.
Other DMMs, like the 34401A / 410A/ 411A have instead 8 x 13k, 1W resistors, which gives 10W in total only, under full overload conditions, which may be applied nearly indefinitely.
The 3458A needs this low ohm input resistance, due to its fast DCV input path.
Frank