The phrase 'increase their capacity' is correct and can be used in written English.
It is used when referring to increasing a person's or group's ability to do something. For example, "The company has invested in new equipment to increase their capacity to produce products."
Companies just are not convinced that they need to increase their capacity yet.
As traffic grew, main routes were improved to increase their capacity and to reduce operating costs.
By increasing people's vagal tone, we increase their capacity for connection, friendship and empathy.
But since the highways are choked with traffic, New Jersey Transit officials are looking for ways to increase their capacity.
Dramatically cut council funding so that as more work piles in, councils cannot increase their capacity to deal with it.
The epididymis secretes substances that prolong the life of stored sperm and increase their capacity for motility.
It looks like everybody makes this decision now because Liverpool and Everton want to increase their capacity and West Ham go to a bigger stadium [in 2016].
Firestone began recommending at the time of the recall that the tires be inflated to 30 pounds per square inch, which would increase their capacity to carry weight.
The consortium core also provides opportunities for members to build their professional networks and increase their capacity for research and implementation through pilot and demonstration project programs.
Others argue that the goal in anti-poverty efforts should be to help poor people increase their "capacity to aspire" and navigate toward self-defined goals.
Educate governments to increase understanding: We organise workshops with the government to increase their capacity, understanding and knowledge of climate change issues.
