Suppose you had an economy where half the agents are "Hand-To-Mouth" and have a Marginal Propensity to Consume of one (Ct=Yt), and the other half are "Autonomous" and have a Marginal Propensity to Consume of zero (Ct=At where At is exogenous with respect to their current income). If the two types of agents initially have the same income, the Marginal Propensity to Consume for the economy as a whole would be 0.5 and so the Old Keynesian Multiplier would be 2.
For simplicity, ignore all other forms of expenditure, and suppose that aggregate income is determined by desired aggregate consumption expenditure (It's an economy with excess supply of goods, where output is demand-determined).
Suppose something causes the Autonomous agents to increase their consumption by 1%. The first round effect is to increase aggregate income by 0.5% (because they are only half the economy). In the second round the Hand-To-Mouth agents increase their consumption by 0.5%, which increases aggregate income by an additional 0.25%. And so on, until the increase in aggregate income converges to 1% in the limit of the multiplier process.
[Update: to paraphrase Kalecki(?): Hand-To-Mouth agents spend what they earn, so Autonomous agents earn what they spend.]
Even though half the agents are Hand-To-Mouth, this economy gives exactly the same results as one where all the agents are Autonomous. The Hand-To-Mouth agents end up mimicking the Autonomous agents.