I've been wanting to post a response but haven't had the time to think this one through for a response.
I am a one man IT department for a mid size non profit, we sell 25% of my time to another non profit 9 miles away from me. In total I am the sole support for about 120 PCs, network, servers, and WAN infrastructure for both organizations. We've been doing this for a little over 5 years now. My first thoughts for considering this option.
1. Be a full time employee for one organization, now you have one executive over you to mitigate issues and be available for a final decision. This also provides you the opportunity for health benefits and vacation benefits, (as an employee you won't necessarily be concerned about AR, billing, payroll and other office expense.
2. Be sure expectations are set and understood, If another org gets 3 hours a week support from you, not all projects will be completed in one week, minor troubles may have to wait a week or two.
3. If you are the IT person for this position or if you are hiring for this position, consider applicants with a broad field service back ground that supported multiple customers in their former life. Each org will have a different personality, management, politics, and work flow. If you are not adaptable in supporting multiple environments, this could become very frustrating.
4. Don't over extend how much will be shared, such as commingling servers, data, purchasing, until you know the relationship is working smoothly.
4a. Do explore common things when possible, one style of smart phone from one vendor would be easier to support than 5 different smart phone models from 4 different carriers.
5. Do create a shared services agreement between the primary and secondary organizations.
Dave