Can we use the amplified signal by the mobile signal repeater as signal source to amplify again by a mobile signal repeater ?

It is not recommended to cascade(use one after another )mobile signal repeaters for further amplification , here is why : 

Decreasing signal quality : each amplification stage introduces noise and distorion to the signal .cascading repeaters can worsen the signal quality ,making calls sound scratchy and data transfers unreliable . 

Potential for oscillation : with two repeaters in close proximity ,the amplified signal from one can be picked up by the other,creating a feedback loop .this oscillation can lead to interference and discrupt cellular traffic in the area . 

Legality concerns : in some regions ,regulations restrict the use of signal boosters and their output power .cascading them might push the signal strength beyond legal limits . 

Alternatives to cascading repeaters :

Using a single ,stronger repeater : if the initial repeater isn't providing enough coverage ,consider a model with a higher gain for your area's signal strength . 

Optimizing repeater placement : ensure the external antenna has a clear line of sight to the cell tower and the internal antenna is positioned strategically within the coverage area . 

Consulting a professional : for complex situations ,consider seeking help from a professional installer who can assess your signal needs and recommend the most suitable solution .