is it possible to further Jewish theology?

I’ve noticed that certain aspects of Jewish theology have changed, like the nature of free will. Apparently the belief in free will has been different over time. Is it possible to still provide insight and help shape Jewish theology?

As you have asked two distinct questions here I shall address them separately.

Is it possible to further Jewish theology?
Yes, this is what every Rabbi, Jewish educator and believing Jew who lives their life with effort of being an example of Jewish ethics, values, and precepts strives to do. We act to further, (used as a verb as in your question above) meaning to foster, promote the growth or continuance of Judaism.
Jews are obligated by Torah to pass along Judaism to the next generation.
All the Jewish contacts and many others I see here in Y/A strive to do this by answering questions about Jewish belief and Judaism to help clear up misunderstandings and provide references for those interested in learning. Jews do not actively proselytize, but are happy to provide reference to learn for any who seek information.

For the second question:

Is it possible to still provide insight and help shape Jewish theology?
Jewish theoogy of course refers to the religion of Judaism.
There are aspects of Jewish theology that have never and will never be changed. There are other aspects that have changed and will continue to change.

The Torah will remain unchanged. It is not possible to alter the Torah. Believing Jews in every generation have taken the commandment prohibiting altering even the tiniest portion very seriously.

How people apply Torah precepts to a changing world means that Jews have had to deal with finding ways to live in congruence with it’s precepts in different lands, cultures, with new technologies and how to maintain our faith, identity and our community in facing new methods to assimilate and eliminate us, as well.
The Talmud itself is a record of the Rabbis struggling to maintain the core and focus of the eternal Torah in the Diaspora through a changing landscape and for all possible scenarios.

Every generation of Jews provides insight into the Jewish religion. We do not shape it, it shapes us.

Aspects of Jewish philosophy have changed over time and often in response to cultural milieu and the focus and emphasis on certain beliefs has waxed and waned, but still through it all, the core of Torah remains as the prophet Micah succinctly stated within the Tanakh, to do justly, love mercy and walk humbly with the Creator.

All our varied opinions and ways of struggling with these issues fit well with our very name and role as a light unto the nations, Yisrael (struggle with God).

Shalom