“Building within a building” is used quite often. The concept also encompasses all structures (homes, community centres, office buildings).
Several examples below.


(1)
“Architecture: Building within a Building
A project to build a modern wooden house inside another building (an 18th century barn), for my own home.”
http://davidgalbraith.org/portfolio/building-within-a-buildi...

(2)
“It’s a building within a building, a classroom within Construction Junction.” November 17, 2015
http://www.nextpittsburgh.com/city-design/project-re_-gives-...

(3 - historical, book)
“… it is likely that the interior shrine was completed first and the colonnades of the great court last…” […] “In the Hellenistic period, the naiskos at Didyma provides a good example of such a building within a building;”
https://books.google.com/books?id=03UNLhtEP1oC&pg=PA23&lpg=P...

(4)
“we have actually realised a ‘building within a building’: a very compact, three-storey complex within the exterior of a building with a prominent roof.”
http://architecturelab.net/design-presented-for-a-new-educat...

(5)
“The architecture was formed by making a clearing within the existing field of structure and filling it with space and light – a building within a building that challenges perceptions of interior and exterior, public and private, old and new.”
www.alliedworks.com/projects/wieden-kennedy-agency-world-he...

(6 - book)
Architecture, City, Environment: Proceedings of PLEA 2000 : July 2000 ...
[Book] By Koen Steemers
“The idea from the civic point of view is that there are different functions within the building and they are unified by the enclosing space. It gives an urban scale and context, which would not normally be expected in and office building. From the environmental point of view the idea is that because the office building forms a building inside a building, there is les heat loss in winter, and in summer the buffer zone is shaded, avoiding the need for external sunshading to the office themselves.” […] “An important aspect of the ‘building within a building’ concept was that windows would be opened into a better environment, warmer than the external environment with the pollution and dust having been largely filtered out.”
[Source: Google Books]
http://tinyurl.com/hcggw4k

(7)
“OMI Architects insert two multi-functional pods into a 19th-century church in Bolton, UK
It is a concept of a building within a building – instead of replicating the original church style, the architects decided to create a contrast and build two volumes raised above the main church floor”
http://inhabitat.com/omi-architects-insert-two-multi-functio...

(8)
“The Civic Center’s main performance hall seats 2,477 and hosts a wide variety of events from traditional Broadway and symphonic performances, to speaker seminars, graduations and fashion shows. Thanks to a 2001 renovation project, the theatre, which is designed as a “building within a building,” is architecturally and acoustically isolated from the original 1936 building structure. The theatre is fitted with a symphony shell that can be acoustically adjusted for amplified and non-amplified shows.”
http://www.okcciviccenter.com/text_only/venues.php

(9)
““Essentially, Salomon is constructing a building within a building – and it's an occupied building, which complicates the situation,” said John D. Spassoff, a district manager of Silverstein Properties.”
“The Salomon Solution; A Building Within a Building, at a Cost of $200 Million”, February 19, 1989, New York Times
http://www.nytimes.com/1989/02/19/realestate/commercial-prop...