If all the conductors are current carrying, then you can figure all 16 of them at 50% of the maximum rated ampacity. Derating is 10 to 20 current carrying conductors to be 50% of maximum rating of conductors.
310-16 shows 35 amps for #10 THHN cu, so 50% of that is 17.5 amps. If you step up to the next higher device rating, that places all conductors on a 20 amp max breaker or fuse.
17.5 amps is the maximum amperage that would be flowing through each of these conductors at one time. If the load is less than or up to 17.5 amps on any conductor, that is OK and can be protected by a 20 amp C/B [even a 30 amp C/B, but that's a little out there]. Protecting the branch circuit with a 15 amp breaker would limit the maximum that could be drawn to at least 15 amps.
Looks like since you have shown 22 amps in your message you will need to either upgrade the conductors for the equipment you are installing to #8 cu, or run a new branch circuit.
Since it is so long, you are better off running a new branch circuit with #8 THHN cu, to overcome the voltage drop of #10s, unless you have figured the volts lossed at 22 amps is not too bad with #10 [seems like it would be excessive just offhand, but maybe it's not].
There will definitely be an excessive voltage drop if all the conductors in that 1" EMT are loaded plus continuous. That will create quite a bit of heat.
If the equipment is to run for 3 hours or more, then do the normal LCL adder to the branch circuit [load]. Either multiply the FLA by 1.25 [add 125%], or derate the circuit's maximum load by 80% and see if the motor load falls in there. Much simpler to add 125% to the total motor load calc [FLA + 125% motor factor, or the listed Min. Ckt Amperage].