The maximum number of lines plotted on a chart depends on how similar or different the data are and what you want to highlight.
You need to make sure that each line is easily distinguished from the others.
Small multiples solution
Use small multiples if it is difficult to distinguish between the plot lines of four or more similar data sets. Use the same scale for all charts when comparing two or more data series.
A singular time series of interest can also be highlighted, with all other data sets toned down.
Slope chart solution
Use a slope chart to highlight changes between selected years. The granularity of the data is not evident, however trends are easily noticed.