Start by naming any country that Lesotho borders. Then name any country that borders any of those countries. Then keep going until the last one, Canada. You got 3 whammies
Gambia | Guinea-Bissau | Iraq | Liberia | Saudi Arabia | Sierra Leone | Spain | Turkey | United Arab Emirates
Country
Andorra | Armenia | Azerbaijan | Bulgaria | France | Georgia | Greece | Iran | Portugal | United Kingdom | Kuwait | Oman | Yemen | Qatar
Afghanistan | Albania | Belgium | Brazil | Germany | Ireland | Italy | Luxembourg | Netherlands | North Macedonia | Pakistan | Romania | Russia | Serbia | Switzerland | Suriname | Turkmenistan
Argentina | Austria | Belarus | Bolivia | Bosnia and Hezergovina | China | Colombia | Croatia | Czech Republic | Denmark | Estonia | Finland | Guyana | India | Kazakhstan | Kosovo | Latvia | Liechtenstein | Lithuania | Moldova | Mongolia | Montenegro | North Korea | Norway | Paraguay | Peru | Poland | San Marino | Slovenia | Tajikistan | Ukraine | Uruguay | Uzbekistan | Vatican City | Venezuela
Bangladesh | Bhutan | Chile | Costa Rica | Ecuador | Kyrgyzstan | Laos | Myanmar | Nepal | Panama | Slovakia | South Korea | Sweden | Vietnam
Cambodia | Costa Rica | Thailand
Malaysia | Nicaragua
Brunei | Honduras | Indonesia
East Timor | El Salvador | Guatemala | Papua New Guinea
I've found a problem with this idea. Even though DRC is a legitimate answer, as soon as I type "DR" I get a whammie (presumably because DR is also Dominican Republic). Are you able to fix this?
I believe Yemen, Oman, UAE, Kuwait, and Qatar should all not be whammys for Andorra | Armenia, if we can go any direction, as long as it borders the last
The exclusion of external territories is normally stated in the quiz instructions. As this quiz did not make any such statement it is reasonable to assume that all borders are counted.