The request for one extinguisher that handles everything is reasonable and the answer is no. No portable agent is rated for every class, and the ones with the widest rating carry the heaviest side effects. What a duty holder can have is a provision, which is a small number of units chosen for the fuels that are actually present, placed where they can be reached.
The widest rating and its price
ABC dry powder is rated for class A, class B and class C and is marked for electrical use. That is the broadest coverage available in a portable. It is also refused in most occupied interiors because a discharge removes visibility almost instantly and the residue gets into everything. Breadth of rating and suitability for the room are two different tests.
What is always missing
Nothing in the ABC range is rated for class F cooking fats, and nothing common is rated for class D metals. A building with a fryer needs wet chemical whatever else it holds, and a building with a magnesium risk needs a specialist powder. These are not covered by buying a bigger general unit.
How a provision is actually built
The fire risk assessment names the fuels room by room. Each named fuel gets an agent rated for it, sized to the risk, at a point on the escape route rather than deep inside the room. Two or three types across a building is normal and is not a sign of over provision.
The question behind the question
Most people asking for one universal unit are trying to reduce training load. That is solvable without a universal extinguisher: standardise on the smallest set of types the assessment allows, put them in consistent places, and sign each point. Consistency does more for a person under pressure than range does.
Questions people ask about all fires fire extinguisher
What does an all purpose fire extinguisher usually refer to?
In catalogues it normally means ABC dry powder. That is a genuine multi class unit and it is still not all purpose, because it is not rated for cooking fats.
Is a multi class foam unit a reasonable compromise?
For a building with class A and class B and no cooking oil and no significant electrical risk, yes. That describes a great many small workplaces.
Does holding more types mean more servicing?
The servicing interval is the same per unit. The cost follows the number of units, which is driven by floor area and travel distance rather than by how many types are in the mix.