Org'n A is planning to apply for a R1 visa. One of our sister organization (Org' B) would like to use his services also for a short time. Can we share some of the services of the person for whom we would like to apply R1 visa. In fact, most of the people of Org'n B are part of Org'n A.
This is unlikely. The person was petitioned by A and needs to work at A minus some narrow exceptions. However, there is no problem getting an R1 to work at A and another R1 to work at B. Please see more below.