The phrase "a small purpose" is correct and usable in written English.
It can be used when referring to a minor or limited objective or goal in a particular context.
Example: "While the project may seem insignificant, it serves a small purpose in the larger scheme of things."
Alternatives: "a minor goal" or "a limited objective."
The stipulation in Turner's will that two of his paintings be displayed alongside works by Claude is still honoured in Room 15 of the Gallery, but his bequest has never been adequately displayed in its entirety; today the works are divided between Trafalgar Square and the Clore Gallery, a small purpose-built extension to the Tate completed in 1985.
The original building was demolished in the early 1970s and was replaced by a smaller purpose-built home which eventually closed in May 2005.
8 The Green House model is a small-scale, purpose-built, aged-care facility that accommodates up to ten residents with high-care nursing needs.
But it is the urgency of small purpose that creates the distraction from mortality.
Even at the height of the firm's success, the entire editorial department (consisting of Keen and a part-time secretary) operated out of a small extension purpose-built at the back of his house.
It uses a small multi-purpose sensor that would attach to a door to detect that it opens, and if it's opening at a time that's unexpected, it may flag the owner that an intrusion is taking place.
There were very few insects riding those currents or in the air, so I tied on a small, all-purpose Parachute Adams and waited for rises, casting when the fish came up a second time.
From the family center, the Ettes and their aunts and cousins took the ferry with other families, several mental health workers and a volunteer carrying a small dog whose purpose was to dispense unconditional love.
This is an inherent problem when tackling process improvement together with a software implementation with a view to making it enterprise scale: deliver a point solution to take care of a specific pain point and you tie yourself in knots further down the line by designing a process fit for one smaller purpose only.
Children use a small number of general purpose verbs, such as "do" and "make" for a large variety of actions because their resources are limited.
