How do I understand how 求められる様に modifies the below?
何度もキスをする Would just just simply mean that they kissed many times.
Obviously 求められる is the passive form of 求める which means to want/request/seek. Since this is in the passive form I think this is referring to the person he is kissing (i.e. the other person is the one doing the verb 求める) but it is still not clear to me what this means.
更に何度も求められる様にキスをする
I think whenever you meet sentences that you think are complex, you should break them down into the most basic parts and try to understand the sentence as you piece it together.
求められる
to be desired for
As you said, this is the passive of 求める. If someone is 求められる, then they are being yearned for.
求められるように
as if (I) was being yearned for.
ように is being modified by the clause before it. 求められる modifies よう here.
求められるようにキスする
kissing as if (I) was being yearned for.
ように modifies キスする. How is he/she kissing? As if they are being yearned for. Obviously, with the lack of context, I cannot give you a very good translation because I do not know who is doing the kissing, but here is the gist of it:
更に何度も求められる様にキスをする
literal translation: (We) kissed multiple times as if (I) was being yearned for.
natural translation: We kissed again and again, as if (he/she) wanted (me).
