[Elecraft] kx3 with amp's

[Vincent Diak]

Dear group,
 I would like some help with my question of can I run two amplifiers in parallel into auto tuner from kx3? The reason is that I want to purchase a 500 watt elecraft amp and also the 500 tuner. I would like to use the tokyo 45 watt amp off the kx3, then into the elecraft 500 amp then into the elecraft tuner. I'm thinking that the relay timing of the kx3, and the other two amps will not function properly as far as the time it takes for the relays to open and close. The 45 watt tokyo has a 5-6 ms switching relay and i believe the 500 amp relay can be set from 0 -50 ms. Can all this work together, and has anyone on here done a similar set up? Another concern is the hook to the tuner?
Thank you all for any support you can give me in this matter!
Yours Truly,
Vincent Diak WB2PDW