It's a little tricky: once you give the Legislature the power of the purse,the momentum of the war between "Court and Congress" swings to the later as they can leverage moments of financial need for more power. And once you enfrancise the financiers/industrualists, they start insisting the government be responsive to their needs if they want loans (which they always did). However, it's possible you could get a softer ceiling that keeps more power in the hands of appointed Ministers by an unbiased monarch if you have a society with highly atomized political influence (IE; strongly multi-party with distinct enough interests to prevent big-tent cohalitions from lasting) . In that case, I could see the Crown being able to leverage their position as a non-partisan power broker to entrench certain areas as under their perogative as to important to be subject to the constant shifting of partisan whims. Basically, turning the Beuracracy/"Deep State" into a bastion of Royal power.
A surviving OE under a modestly more liberal Abhul Hamid seems like a good choice here, or maybe a Meijji Japan that comes into power via slow evolution/co-opting of the Tokugawa state apperatus (Silent coup rather than Boshin Wars) instead of adopting the British model. This could create a template other "Eastern" rulers might adopt if successful, which could create a mutually supporting web of political theory strong enough to renforce itself against egalitarian challenges. A defense against the "Tyranny of the 50%+1, per say.