Not if you want to use thermocouple to measure temperature accurately.
When you join the dissimilar types of wire, you will create more thermocouples which will affect the voltage you measure at the instrument end of the wires.
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"Love justice, you who rule the world" - Dante Alighieri
Omega Engineering has some very helpful information online. This paper, "Using Thermocouples" (PDF) includes the subject of thermocouple extension wire.
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