还能再要signing bonus, 但是, 不要也罢

Since you already did the necessary negotiation, and you got the salary as you want.
And you did forget the sign-in bonus.
Unless you want to play the hard ball and you don't care too much about the offer, it is not necessary to ask those so called singn-in bonus.
Many company do not offer sign-in bonus.
Many company ask you return the sign-in bonus if you resign in 1 or 3 years.
Therefore, be happy for what you already get.
Enjoy what you get and be happy with every minute!
Thanks! 美国老土 俺可没说让您看