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The phrase "all three institutions" is correct and usable in written English.
It can be used when referring to a specific group of three institutions that have been previously mentioned or are known in the context.
Example: "The report highlights the contributions of all three institutions in advancing research and education."
Alternatives: "the trio of institutions" or "the three organizations."
Exact(43)
Even today, all three institutions remain separate.
All three institutions suffered from political interference.
All three institutions simultaneously exhibited those collections in 1998.
All three institutions have exceptional collections of drawings.
When Parliament is referred to in some formal usages, all three institutions are included.
At all three institutions, Dr. Frei also trained a generation of researchers and clinicians.
Similar(17)
An estimated average travel and waiting time of 10 minutes respectively was rated as acceptable by HSUs from all three institution types.
All four institutions received federal bailout money.
All four institutions vigorously defend the association.
All four institutions have vigorously defended BP's involvement in the arts.
A statement on behalf of all four institutions said: "We are grateful to BP for their long-term commitment, sharing the vision that our artistic programmes should be made available to the widest possible audience.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com