Suppose we have a uniform rectanglular grid as shown below. The a is an agent, o is obstacle and g is goal. What are the options of handling multitile agents (e.g. dragons or tanks)?

.  .  .  .  o  .  .  .
.  .  .  .  o  .  g  .
.  a  a  .  .  .  .  .    <-- too tight
.  a  a  .  o  .  .  .
.  .  .  .  o  .  .  .
.  .  .  .  .  .  .  .    <-- should go through this gate
.  .  .  .  .  .  .  .
.  .  .  .  o  .  .  .

Suppose we have a uniform rectanglular grid as shown below. The a is an agent, o is obstacle and g is goal. What are the options of handling multitile agents (e.g. dragons or tanks)?

.  .  .  .  o  .  .  .
.  .  .  .  o  .  g  .
.  a  a  .  .  .  .  .    <-- too tight
.  a  a  .  o  .  .  .
.  .  .  .  o  .  .  .
.  .  .  .  .  .  .  .    <-- should go through this gate
.  .  .  .  .  .  .  .
.  .  .  .  o  .  .  .

Update: Found this article on clearance-based pathfinding from Red Alert 3. It covers not only the clearance - size, but also a capability - ability of certain units to use certain terrains.