We've discussed this a little in the Office Space Conversion thread. Basically, Sierra Place (originally the Dome building) was built as shown on the left in that tweet in 1958 as a four story building, the same year as the landmark
Elveden Centre across the street (and in a similar style). In 1980, six more stories were added, but they are fairly consistent in look with the bottom four rather than a Biscuit Block (etc) totally different style.
This link has more history of the building. There are a handful of good ca. 1958 International style buildings in the area; in addition to Dome/Sierra Place and Elveden Centre, there's the
Britannia Building across the alley from Dome/Sierra and the
Petro-Fina building across the alley from Elveden. This area was really Calgary's first downtown of the post-war/post-Leduc oil boom era.
To me it's a pity to lose the heritage facade of the building, but I suppose push come to shove I'll take more housing units than an empty heritage building, if both are not possible.