...どおし => Throughout N3
Continuous
におかれましては => in respect of; in regards to; as for N1
Emotional
お~願います => please do (A) N2
~かとおもえば...も => no sooner than N1
Compare
~とおもうまもなく => Suddenly~ N1
Right after...
~どおしだ(通しだ)      => do something all the time N1
いたします => to do (polite form of します) N4
…とばかりおもっていた => Thought that ... N3
Speculation
ました => Did something... N5
Conjugate verbs
... します => Make... become N4
Purpose, target
おまけに => A. In addition, B N2
(Not)only, (Not) even
~をおして      => to overcome (opposition); to push past ~ N1