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иметь много дел stresses
gen.	have many demands of time; have a lot on one's plate (Анна Ф); have many demands on time
ed.	have one's work cut out (alexghost)
idiom.	have one's plate full (Christina_Evseeva)
Makarov.	have many demands on one's time; have much work to do; have very much to do; have one's work cut out for one
имея много дел
gen.	having much business in hand

иметь много дел: 7 phrases in 3 subjects

General	5
Informal	1
Makarov	1