A weak Product Management function can result in features that are not introduced in response to customer needs but in response to internal wish lists (that may be out of touch with the market), or in cost structures that are not being revised strategically to enhance profit margins (like outsourcing vs. internal development). To change a Product Management function takes making an assessment, mapping out where we are today, where we want to go be and what are the best practices in what we need.
After the initial assessment and once you understand where you are and where you want to be. Choosing the right framework will be one key to your success. There are several frameworks about what Product Management should be, for example: the PDMA model has one, author Steven Haines documents another, and author Marty Cagan shows us yet another one. All frameworks list a set of skills and functions that every organization should have. But just using any of these frameworks will not work for a company, as with everything in life, each situation is unique and your framework should be tailored to your needs. Best product management practices will come from a consultant (you are hiring one, right?), current literature and studies on the matter.
Another big factor is if your company wants to change its culture – for example, is the organization willing to let a Product Manager team define and control the product? Or are they convinced that it is a function of the Marketing department? Whatever the answer to the culture question, it will mean a lot of changes to marketing, product development, service desk, platform development, etc. If your company is not willing to change the culture, the best way is to look for a framework that will reinforce current weaknesses and strengthen what is being done today.