I suppose most of their work would fall into the unacceptable category, but
Torti Gallas is worth looking at. Most of their work is not strictly historicist, but rather combines contemporary materials with traditional design concepts. They produce buildings like
this one that are distinctly contemporary, but not modernist. They know how to use the right materials and proportions, so unlike what some may call "faux", their stuff usually looks great.
Moving on to some examples of things that do qualify from Washington, DC:
The Kennedy-Warren apartment building is one of Washington's most important art-deco buildings. It was originally built about 1930. In about 2002 the owners decided to expand it. The expansion has a contemporary interior layout, but matches the original exterior exactly. Aside from the difference in weathering, you cannot tell the 21st Century portion from the 1930 portion:
Main entrance:
source
Detailing from 1930:
source
Detailing from 2002:
source
Another potential example that comes to mind is the National Cathedral. It took over 80 years to build, but was not completed until 1990. Many of the details were designed and constructed in the 1980s.