どうかよろしく
Meanings
1
please remember me; please treat me well; I look forward to working with you
usually written using kana alone
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
I humbly ask for your kind favor.
Everyone in the new department, I look forward to working with you.
2
please do; please take care of
usually written using kana alone
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
Please take care of this matter.
I earnestly ask you to handle it.