It's a possibility from the bigger towns that are along the route: Santarem, Tomar, and Coimbra all have major bus stations that are hubs for the smaller towns surrounding them.
What you may find problematic is that typically, for the smaller towns, the local buses run from each one to the bigger hub in the mornings, for high school students, workers, and commuters; and then run back to the smaller towns in the evenings.
It's probably best to look at hopping between two of the larger places. That will typically use the railway, CP, rather than the bus, since the local authorities are reluctant to subsidize a bus service where there already is a good railway link that costs about the same.
CP website (easy to use!):
https://www.cp.pt/passageiros/en
Their network map (not so easy to find!):
https://www.cp.pt/StaticFiles/Passageiros/3_viajar/0_servicos/mapa-servicos.pdf To hop from town to town, you'll usually want the Regional service marked in red. It stops at all the small stations, and is a bit less expensive than the other services. No reserved seats, as a rule. A great service!
A more simplified map is here:
https://www.cp.pt/passageiros/en/how-to-travel
f you are committed to the bus, Santarem to Fatima is a good bet, and then a local bus from Fatima to Tomar or Fatima to Coimbra. Because of its religious significance to the Portuguese and location off a railway line, there is an unusually strong network of buses between the bigger towns/smaller cities and Fatima.
Bom Caminho!