I'll have a stab at answering this (from a purely theoretical perspective rather than suggesting specific solutions). Apologies for the lengthy response - The below is industry-agnostic, but much of the research and experience is from the IT industry (software/saas, MSPs, IT project providers etc.). The scope is SMEs only (200+ pax is a different kettle of fish).

Short answer: not really.

Long answer: The following is an assessment of what such an 'open framework' should/would/does entail - Including turnkey modules for such things as DevOps / Helpdesk / Procurement etc.

While contingency theory (https://en.wikipedia.org/wiki/Contingency_theory) states that there is no standard way to organise a business, I believe that there is actually a basic framework that could underpin all capitalist enterprises.
This needs to be malleable and allow for variables, but there is a simple holistic structure that all companies essentially fit.
This framework would be valuable to:

- Provide an overarching, comprehensive view of the company for peace of mind and understanding

- Dictate the systems and process to achieve end products in all areas of the business

- Identify what functions have not been codified, or are in need of improvement (e.g. a Data / Security module may show that a company does not yet have a Data Controller / GDPR procedure in place).

- Be the single source of information (i.e. no rogue manuals being created by staff, no going 'outside of procedure' if it is codified).

Common vernacular across all industries offering such solutions is "a business process" - But it is rare to see the phrase "ALL business processes" catered for. An organisation's documentation / manual / processes are rarely up to date, and no companies seem to offer a comprehensive business framework. Management Consultancy rarely deals with a business 'holistically' (But this strays into a conversation regarding issues with the Management Consulting industry, which is a topic for another time).

Further, there is no consensus in industry as to a comprehensive business manual (i.e. all business processes collated, all activities catered for).
On top of this, there is no consensus as to categorisation - I.e. sorting this common framework into a business processes and organisational structure that everyone understands.
There are many 'business operating systems' and 'business frameworks', but their names always oversell the scope of what the product actually does - Most will simply be a small collection of tools for management or the product lifecycle.

There are business problems (for SMEs) that have existed for thousands of years, but have had solutions for nearly as long. Yet, those problems still exist.
Has a waiter ever forgotten something for your table? This should be a solved issue (problem: human error, example solution: notepads with categories including 'miscellaneous requests'). But most restaurants reinvent the wheel to some extent.

The above paragraphs lead to this hypothesis:
"A business framework could be provided which reduces overhead for SMEs, providing them direction and structure and preventing them from having to reinvent the wheel. The framework would be a living, breathing system, allowing for continuous improvement and preventing issues with existing solutions."

So why does the above not seem to exist? (If anyone knows of any relevant existing solutions here, I would love to know about it).
I suspect that it is partly this: Capitalism is still immature/changing, so there is no stable framework yet - even at a macro view.
An example manifestation of this is that 'IT' was shoehorned in as a major department over the last 30 years. Researching into Organisational Structure shows that really, we haven't even figured out how to categorise a company's activities. Without going into too much detail, consider Finance and Operations vs the IT department. IT is far too small in theoretical scope. It deals with the technology of a firm only - Arguably, an IT department should be an 'internal systems' department that provides ALL resources and systems (e.g. rather than just technology, this department should also be suited to providing pens, paper, chairs, desks, and other non-tech tooling to help undertake a task). It's all the same - Providing the system and process for the company to undertake activities. 'Uptime' and 'availability' is as relevant for chairs and other items as for IT systems.

To summarise - I have spent 15 years looking for such a thing, and it simply doesn't seem to exist to the extent needed.
Therefore I am creating my own. I feel as if I am pioneering - There really is so little precedent for me to lean on. However, I am convinced that there is a solution here - The reason it doesn't exist is NOT due to it being impossible.

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I have put some misc notes here, as they may be relevant to the conversation.

Many frameworks and organisational structures fail to explicitly identify Supplier (or partner) Relations. This is a core component of many businesses. Presumably Supplier relations is usually implied within either Strategic Management or Procurement. Porter (Porter's Value chain (1985) - https://www.ifm.eng.cam.ac.uk/research/dstools/value-chain-/) identifies this within the 'inbound logistics' process. However, this fails to holistically cater for the entire supplier lifecycle, or do justice to its scope or importance. For example, Supplier sourcing may include a diligent tender process with credit checks and shortlisting. It may also involve ongoing relationship activities to maintain the contract.

Similarly, Porter's Value Chain can be seen as under-catering for the importance of Community Relations. Marketing and Sales is bundled as a core process of delivering to the consumer. However, Marketing should be seen as much more than this. Rather than being tied to sales or customers, in this century we should acknowledge that a modern business needs to have a mechanism for interacting with the community regarding many things other than specific Sales - Community participation, market feedback from stakeholders other than customers, PR regarding company changes or other events that are not sales-driven, etc.

[side note: Proponents of Porter's Value Chain would argue that this is miscontruing the purpose of the tool. My counter-argument is that the Value Chain model does not fulfil requirements as well as a different-view framework would].

Current org structures don't cater for future needs in the free market. E.g. If trying to add an 'ethics' function - Where to put it? Many would place it in the Executive department/pod. Many would shoehorn it into Finance (as finance are assessing risk and identifying externalities, they can do so for things other than fiscal value). Regardless, current Org Structure theory appears stuck in a legacy 'capital only' mentality - They don't cater for 21st century Capitalism, where the consumer is starting to demand things other than just quality product + low price.

Most business operating systems, business frameworks etc. do not provide an overarching, binding solution to all of an organisation's tools and processes. Their scope is small, and just adds another tool to maintain for the business.

- EOS for example is a leadership or people management tool. It is very macro - I.e. it does not provide solutions to anything specific other than some HR and management exercises. (https://blog.eosworldwide.com/blog/what-the-heck-is-business...)
Orca comes close with its philosophy but falls short with scope and cohesion/categorisation

- Many management consulting firms will tout a BOS, but without an actual system/framework to support it - And those systems that are provided are lacking in scope. (http://www.orcabos.com/what-is-a-bos/, https://www.qpr.com/solutions/business-process-management, https://www.quickeasysoftware.com/business-operating-system/)

- Lincolnshire council (UK) does a good job (HR department only) of exposing all procedures ready for compilation into a BOS.
https://www.lincolnshire.gov.uk/jobs/manuals/employment-manu...