Creating a new SE organisation, or working out how to structure it so that SEs can work well as a team, and also with Sales Reps, Branch managers and other staff is a challenge for any organisation.
Part of the issue is that SEs tend to be sparsely spread across all geographies, with varying skills across the product set. Also it tends to be that there is a difference between being a good SE, and being a good Manager.
For a small organisation, having up to 5 SEs, all members of the team have to be actual SEs, able to fulfill the role themselves. Most organisations would structure it so that one behaves as the team leader, or in footballing terminology a player-manager. Being a team, the manager's role here is not the full A-Z manager who checks expenses, knows everything each member is doing all the time or general babysitting. A Player-Manager is also just as concerned at fulfilling their own role, and the extra part is spent ensuring the rest of the team are connected to technical resources they need, are working well with their local organisation, ask for help when they need it and so on.
Realistically the player manager is an enabler to make sure that the SEs do behave as a team, that their skills are effective and interchangeable and that the sales organisation has what it needs to succeed. Another important role for the Player-Manager is hiring new SEs and ensuring that their team is ready for the scale of the sales efforts ahead.
As the company develops and the team expands towards 10-20 members, there will be an organisation shift. There will effectively be too many "players" for a "player-manager" to handle. It could also be that the Player-Manager is a better player than a manager or vice-versa. So the organisation would shift to having a full time manager (although some managers may remain player-managers), and as it grows further it will need more managers and even an SE Director.
To balance this out, these Managers don't necessarily have the same skills as the SEs, and depending on the organisation, there may be SEs who are extremely important to the company as SEs. These may become Lead or Senior SEs and may not head into a manager role unless they really desire that and reskill.
Depending on the product set, SEs may need to specialise so that the organisation is able to call upon experts on particular products, and with this many SEs there is often the luxury of having more than one at a particular office location.
In this size team training becomes an important thing (see Training for sales engineers), and a team trainer is needed to develop training programmes and material. The other part of this training is that the team needs to consider the evolution of its members and their succession within the organisation. Good team players who have potential to manage or lead others should be nurtured and kept within the organisation.
Finally, a massive organisation will have hundreds of SEs. This calls obviously for more specialisation, and also division within the organisation into units. Now there will be more Directors, leading teams of up to 30 SEs and managers. There will be managers in each region below them, and they would all report up to a Head of SEs, or VP of Sales Engineering (SEVP). Again training will be important. There would be dedicated inside roles for working on RFPs and Bids. Each product may have a Lead SE who works exclusively on that product and develops demonstration materials on that. Even Industry verticals or partner specialists would be good ways of dividing the team.
Given that large organisations tend to have larger barriers between divisions, it is necessary to
ensure that the SE organisation has access to the latest product, development engineers, marketing, the sales organisation and upper management, and this needs to be through dedicated resources to keep the business running smoothly.
For further reading on how to structure or organise the SE team, I highly recommend the book Mastering Technical Sales: The Sales Engineer's Handbook (Artech House Technology Management Library) by John Care, Aron Bohlig.