Please make a stop on your way home.
The sentence can basically be split into two concepts: (request to perform action) (during pre-ordained action).
The pre-ordained action in this case is the action of travelling from the current location to your place of residence - "on your way home".
The request to perform another action at the same time in this case is "make a stop", and this is what is the most ambiguous.
"Making a stop" can mean many different things depending on the context. The context is partly defined by the pre-ordained action that is occurring at the time it is requested that you perform this additional action - in this case travelling home.
So that rules out things like crafting a Vox Humana Stop for a pipe organ.
So it implies a break in your journey for some other (undefined) action to take place. Exactly what stop means in this situation is dependent on this third unspecified action is.
For instance, it could imply:
- Could you stop off and pick up some washing powder on your way home? - a brief pause in your journey for you to perform a third action.
- Could you stop off at the video store so I can pick up a film? - Another pause in your journey whilst your passenger performs an action. The time-scale of this action is not now as much within your control since it may take them some time to decide which film to rent.
- Could you stop off and see me on your way home? - Again an action you would have to perform during your journey but the time-scale of the action can be out of your control since the third party requesting the visit can dictate what happens during the visit.
Without knowing the context in which the request takes place it is not possible to predict more about what the action would likely be. For instance if your wife phoned you at work she might be requesting that you pick up some washing powder on the way home (1). Maybe you regularly provide a lift to a third party home from work (car sharing) and they may want to watch a film tonight (2). Or maybe your Mother has a birthday present for you to collect for your son (3).
Given the phrasing of the request and the action to be performed during the stop is unspecified it is most likely the second option above where you are providing transport to a third party and it is their sub-action that will be performed whilst you wait for them to complete the journey. In this case the question is more often (politely) phrased as:
Do you mind if we make a stop on the way home?
Do you mind if we make a slight detour on the way home?
The addition of the word we includes the third party in the travelling arrangements.
It is important to note that these are all temporary pauses in your journey and that your journey continues to completion after the interrupting "stop" action has been completed.