Going off on how Perez is, I think he'll support her because he loves her (or I hope so lol, didn't read the novel) or possibly change the law. Tia has always wanted to be the head and I think even Perez knows her love for her family is more/ or even equally the same love she has for him. (I think I will drop if her goal wavers, because I'd hate to see her hard work crumble for a guy- even if its Perez lol.)
perez would never do anything that would intentionally hurt tia or their relationship. tia made it clear to him that being lombardi’s matriarch is very important to her so perez would make it happen. in one of the chapters, perez implied that he will make sure tia achieve everything she wants to achieve while also serving as an empress beside him.
The law will change. After the emperor got poisoned and was bed ridden and Perez kinda became the default crowned prince..
Perez gave the emperor an ultimatum (sorta)... either he will be emperor OR it would be (1 armed and mentally disabled....?) Astana OR a VERY distant relative who didn't even bear the surname Lambrew.
The emperor was so mad at Perez and asked him if it was because of "that b*tch" and Perez answered that everything is for Tia or nothing at all.
What Perez was asking for was that the emperor make his final edict (like their dying wish) to say that females who mary into the royal family will still retain their title and land and rights and inheritance (w/o the crown benefiting from it) and surnames.. this law permits Tia to become both the empress and the matriarch of Lombardi and the Lady of Chesayu.
Perez can't change the law himself even if he becomes the emperor coz when he does, it would be for the next empress and not HIS empress. So that's why he needed it to come from emperor Javaness.
The emperor's edict is kinda like a very powerful last trump card of the ruler that would make everyone do anything that the emperor wants. Normally it was like for their funeral to be grand or for that sort ot thing.... they needed to honor it no matter how absurd it was.
Jovaness threatened Perez that Astana would be emperor and Perez only said "okay. I'll send a letter to retrieve him from the front lines then."
Javaness told Perez that he was such a stupid child and that one person wasn't worth that much. Wasn't worth to give up the throne, crown and riches over. He also asked Perez what would be his plan if he gave up the crown.
THIS IS MY FAVORITE PART:
Perez proudly and nonchalantly said "I'll be a live in son-in-law of the Lombardi."
The emperor was so f*cking flabbergasted at the absurdity of it all.
Imagine, only a few weeks and Jovaness would die and the next in line would give up being the emperor just to become a live-in-son-in-law
Jovaness eventually gave up and gave Perez what he wanted.
So technically Perez didn't change the law. Jovaness changed the law for Perez

I know Tia said that because of her relationship with Perez she would never forsake the family name, but we know that Perez is obsessed with her. So my question is knowing what Tia wants and that being to become the matriarch, will Perez let her be or would he try asking for her hand in marriage knowing she would probably say no even if it will hurt their relationship?