Charles Rennie Mackintosh's Renfrew Street masterpiece is to be extended – but not everyone's happy

Charles Rennie Mackintosh is a British rarity, an architect who led rather than followed, who was admired and studied abroad, and who influenced the direction of the world's architecture. More often, this island breeds skilful latecomers to continental movements, such as Inigo Jones, or great originals whose influence goes nowhere, such as Nicholas Hawksmoor.

Mackintosh's masterpiece is the Glasgow School of Art of 1897-1909, later hailed as a precursor of modernism on account of its simplicity and abstraction, but which is far more than a diagram of the future. It is a building of dazzling range and freedom, from its massive, castle-like south side to the filigree metalwork on its north. It is robust, as an arts school should be, still taking a daily beating and splattering from students, but also exquisite. It runs from bare concrete and painted softwood to leaded stained glass and intricate carving and joinery. Its inspirations extend from Celtic and baronial to Michelangelo and the Glaswegian industrial might of Mackintosh's own time. Every part breathes the independent spirit of the policeman's son who was 28 when he won the commission to design it.

The school is a Scottish national treasure, like a more fascinating Stone of Scone, and an object of veneration by architects all over the world. Now it is to be extended with a new building across Renfrew Street from its north facade. Following an architectural competition, a well-respected American architect was chosen, whose proposals will be considered by Glasgow City Council's planning committee in nine days' time. Yet dissenting voices have been raised: historian William Curtis calls it a "monstrous intervention". Murray Grigor, who has made three films about Mackintosh, calls it "a cliff of glass".

Much has been done to achieve an outcome worthy of Mackintosh. Steven Holl Architects were chosen by a competition jury led by architects, rather than the project managers who usually arrange these things. The new building is to be constructed with old-fashioned building contracts, which give a higher degree of respect to architects' intentions than the contractor-led deals that are more common nowadays.

Holl, who is based in New York, is an architect with an aura of seriousness. He gets up early every day to paint, usually in watercolour. He invokes philosophy and science and endows his projects with poetic names, such as Writing With Light House or The Tower of Silence. He ponders the qualities of daylight and of building materials, their roughness, smoothness, patination and porosity. He likes the word "haptic". He says things such as: "Building transcends physical requirements by fusing with a place, by gathering the meaning of a situation."

He has visited Mackintosh's works and studied their spaces and light. He has identified the palette of colours used in the School of Art and come up with a complementary one for the new building. He has painted evocative watercolours of the airy studios he wants to create there. He has worked and reworked the positions of stairs and the shape of the building. His office has run computer simulations of its lighting effects, inside and out.

His design is based on a series of well-lit studios connected by ramps and galleries where students can, as they do in the internal warren of Mackintosh's school, pause, meet, reflect or rest. There is to be a south-facing terrace, with planting inspired by a machair, which is a kind of peaty coastal pasture. The exterior, composed with the harmonious proportions of the golden section, is in green-tinged matt glass, intended as a foil to the reddish stone of the old building.

Yet, for all this due process and care, Curtis says: "It is horrendously out of scale, it dominates Mackintosh, it does not create a decent urban space, it fails to deal with the context near and far, it is clumsy in form and proportion, it lacks finesse in detail."

And, looking at the confrontation of the old and proposed buildings across Renfrew Street, it's hard to see the evidence of all Holl's thoughtfulness and attention. The new follows the approximate shape of the old, but it is bulked up and coarser-grained. It makes its moves in increments of metres rather than the fractions of inches in which Mackintosh worked. It looks like the old building's robotic cousin.

One of the marvels of Mackintosh is the way his building varies on every front, in response to different settings, while keeping an overall integrity. The Holl design is more monolithic, with a narrower range of notes. This exaggerates its bulk, making it into a single conspicuous object. The hard, sharp, bright glass, meanwhile, threatens to outsmart the weathered stone of the old, turning it from mellow into shabby. Holl's team say the glass will be subtle and respectful, almost like alabaster, but it's hard to be confident about this from the available information.

It is not that the new has to bow and scrape to Mackintosh. A contrasting material is better than a pale shadow of his unrepeatable stonework. There is much to like about Holl's interior: his studios and his idea of making social places out of the stairs and galleries that connect them. But outside there is no sense of rhyme or rapport between the two buildings. This is not a project that needs ripping up and starting again, but it needs a lot more work if it is to be equal to its good intentions and of the ghost of Mackintosh.