*The naivete of Democratic Socialism is that a fundamentally capitalist country can actually be transformed step-by-step into a socialist or communist society. Reforms are helpful, they can increase the political and social power of the working class, but as the working class gains power they come into increasing conflict with the capitalist class. Every time this conflict has become sharp, the Democratic Socialists have come down on the side of the capitalists. Furthermore, Democratic Socialists seem all to often to early on want to take power away from the hands of the working class to prevent this conflict. As Elena Kagan documents, at the first victory the Democratic Socialists gave away the New York City garment unions' power to strike.
First, what do we want to keep? Nobody is wrong all the time, and republican capitalism has achieved some notable innovations that seem worth keeping, with perhaps some modifications.
The first worthy innovation is the rule of law. (What makes the rule of law a "bourgeois right" is not that it's wrong, it's that it's too limited: we have to consider the content of the law, not just the fact that we have any law at all.) The rule of law means that the government — even a democratic government — has to govern by consistent rules that have to be applied according to objective criteria. The rule of law stands opposite to personal rule, i.e. governance according to the day-to-day opinions of some privileged person or persons.
You cannot have the rule of law unless you institutionally separate the formation of law from its interpretation; otherwise, you just get personal rule in the interpretation. Thus we have to have a more-or-less independent judiciary. We would probably need a wholesale replacement of individual judges, but we can keep the present-day judicial structure largely intact. At the community level we have judges elected directly or appointed by an elected body for a fixed term; at the appellate level we have appointed judges with lifetime tenure. This structure would be advantageous for a magical in-place communist revolution, insulating for a time a communist constitution from the influence of unofficial capitalist-based social and political constructions remaining in society.
The second innovation, related to the rule of law, is establishing constitutional protections for individual and minority rights. There are certain principles we need to strongly insulate from even the majority, most specifically the power of a minority to attempt to become a majority. We can, in fact, keep the existing Bill of Rights virtually intact, tweaking only the Second Amendment to make it less ambiguous* and the Fifth to distinguish between personal property and the ownership of capital. I would additionally incorporate the UN Declaration of Human Rights, again distinguishing personal property from capital in Article 17.
*I'm in favor of the Second Amendment — the armed proletariat is a crucial component of communist theory — although I have some issues with its present interpretation. I read the "well regulated Militia" clause as broadly permitting government regulation of the ownership of firearms, such as registration, mandatory training, and safety and security regulations. I would even go so far as to say that it would be legitimate to require membership in an organization establishing military discipline, so long as membership in that organization was a broadly protected individual right.
Although it's hardly an innovation of republican capitalism, we are compelled, I think, to keep a civil service: every civilization since the invention of writing has had a more-or-less distinct civil service, increasingly operating according to quasi-legal rules established by a policy-making body. Even private organizations of more than a few dozen people include a bureaucracy. Indeed bureaucracy might well be a sine qua non of civilization itself. We need to maintain an institution that knows how to "turn on the lights", and a stable civil service acts as a dialectical counterweight to volatility of popular sentiment. In any event, I'm unable to think of an plausible, practical alternative. I will, however, propose substantial changes to how the civil service should operate.