expression
please remember me; please treat me well; I look forward to working with you
A polite request for goodwill, often used when introducing oneself or asking for future cooperation. Similar to よろしくお願いします but with どうか adding a stronger, more earnest tone.
See also: よろしくお願いします
どうか宜しくお願いいたします。
I humbly ask for your kind favor.
新しい部署の皆様、どうか宜しくお願いします。
Everyone in the new department, I look forward to working with you.
expression
please do; please take care of
Used when earnestly asking someone to handle a matter or take care of something. The どうか adds a pleading or heartfelt nuance.
See also: よろしくお願いします
この件、どうか宜しくお願いします。
Please take care of this matter.
どうか宜しく頼みます。
I earnestly ask you to handle it.