What are the risks of aquiring multiple companies in various regions in a short time frame?

part of the benefit of acquisitions is to reduce costs through economies of scale:combining certain processes across the companies. in the situation you describe, there is both a time and geographic hindrance to doing this in an efficient and effective manner. for example-

1. different logistics/supply chains difficult to quickly integrate over distance

2. different markets/diversity means higher learning curve, so marketing/sales techniques may not be able to be combined without lengthly research.

You have been given some great points by Wisdominknowledge.

The main drivers of the strategy you indicate would be the macro and micro economic factors of the market space and the product space. All this would then be weighed against the budgetary constraints and the human capital available to the organization doing the acquisitions.

Under certain circumstances rapid expansion via acquisitions is a good pre-emptive strategy to reduce competition and threats of new entrants.

Whereas there are circumstances when growing internally to expand into various areas is better suited if the organization has strong brand image, infrastructure, human capital, financial capital etc.

Economies of scale is a very valid point if the business you are entering lends itself to the construct. Centralized vs regionalized process would have to be weighed along other risks and benefits of market expansion.

Assimilation of varied business units under one umbrella needs skills for smooth transition.