The phrase "a second organization" is correct and usable in written English.
You can use it when referring to an additional organization in a context where multiple organizations are being discussed.
Example: "After reviewing the proposal from the first organization, we decided to also consider a second organization for our partnership."
Alternatives: "another organization" or "a different organization".
A second organization has announced plans to create a sport out of competitive cheerleading in an effort to get competitions recognized by the N.C.A.A.
A second organization with a somewhat different approach to practice, the American Association for Music Therapy (originally the Urban Federation of Music Therapists), was begun in 1971.
An earlier incarnation of the group led the push for the Oregon law, and it is now helping, along with a second organization, Compassion and Choices, to promote the Washington measure.
Last year, the Judicial Crisis Network and a second organization it donated money to bought political advertisements in two Supreme Court races in Arkansas, which are decided directly by voters.
Even before the collegium's first concert, he espoused grand visions in The New York Times: "I'd like to jump over the Classical and early Romantic repertory and have a second organization, called the Romantic Orchestra Project, that would begin with the 1840's and move up through Wagner".
Following the success of VALID International, Collins established a second organization, VALID Nutrition, in 2005 to develop products for the new RUTF market that he had helped create.
The prosecution has specified Al Qaeda and one of its affiliates, as well as a third organization whose identity, also disturbingly, it classified.
A third organization, the Center for Immigration Studies, joined the others in December in defeating the Dream Act, which sought to legalize some people brought to the United States illegally as children.
He also banned a fifth organization that, he said, had lured thousands of young Pakistanis to "massacre" in Afghanistan, in defense of the Taliban during American attacks.
A secondary General Staff has recently been set up to deal especially with the procurement of matériel, and a third organization, known as General Headquarters, to handle the units in the field as they come into being.
The second version of IESMR was used to evaluate the measurement repository of a third organization.
