Thank you so much for you kind words. I am going to post the verses here which tells us who is prohibited in marriage so we can see who we are permitted to marry.
Chapter 4, verse 22-23
Do not marry the women who were previously married to your fathers - existing marriages are exempted and shall not be broken - for it is a gross offense, and an abominable act.
Prohibited for you are your mothers, your daughters, your sisters, the sisters of your fathers, the sisters of your mothers, the daughters of your brother, the daughters of your sister, your nursing mothers, the girls who nursed from the same woman as you, the mothers of your wives, the daughters of your wives with whom you have consummated the marriage - if the marriage has not been consummated, you may marry the daughter. Also prohibited for you are the women who were married to your genetic sons. Also, you shall not be married to two sisters at the same time - but do not break up existing marriages. GOD is Forgiver, Most Merciful.
These verses address men but the rules apply to women too. So, no one your father was previously married too (step mothers), no close family members, it says sisters but it does not say step sisters. A half sister/brother would be a close relative but a step sister or brother is not a blood relative. They are from another family and not related.
I have read on other websites about Islam that marrying a step sibling is forbidden, but I cannot find that statement in the Quran.
I would say, yes we can marry a step sibling as we are not related by blood and I cannot find anything in the Quran that says otherwise.
I hope this helps.