The proposed three-obtuse example totals \(360^\circ\) and has one acute angle, so it is possible.

Four obtuse angles would total more than \(4\times90^\circ=360^\circ\). This contradicts the quadrilateral angle sum.

Answer

Three: yes, for example \(100^\circ,100^\circ,100^\circ,60^\circ\). Four: no.