In this paper we examine the benefits and limitations of mechanism design as it applies to multi-agent meeting scheduling. We look at the problem of scheduling multiple meetings between various groups of agents that arise over time. Each of the agents has private information regarding their time preferences for meetings. Our aim is to extract this information and assign the meetings to times in a way that maximises social welfare. We discuss problems with previous attempts to design incentive compatible (IC) and individually rational (IR) mechanisms for the task. We focus on the problem of determining when agents are available. In particular, we show that when agents with general valuation functions are asked to supply their availability for meeting times, there is no IC and IR mechanism. Given this impossibility result, we show how the likelihood of violating IR can be reduced through agents expressing their value for the presence of others at meetings. We also show how requesting agent preferences for entire schedules helps to eliminate IC problems.