Whether or not there are a lot or a few service departments will not impact the use of similar or different overhead rates. If all of the service departments incur costs in the same manner, then one rate is appropriate. If there are only two service departments and their costs are incurred differently, then different rates should be used.
Whether the overhead costs are fixed or variable does not impact how the overhead should be allocated.
When the activities in the plant are different (not homogenous), it is best to use different overhead allocation rates for each department. This will lead to a more accurate allocation of overhead costs than if the same rate were used for all departments.
If all products require the same manufacturing effort in each department, then a single rate can be used. This will be easier and also provide the same allocation as if different rates were used in each department.
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