However, if the heads get to 4c on a takeover event.Then they...

However, if the heads get to 4c on a takeover event.
Then they are limited to the intrinsic value of 1c.

Unless you can make the case that it will get to 4c, without that. Then yes, the ops could trade higher than their intrinsic value, expecting any take over to be higher than that the market is paying..

But 4c means 120m MC. FD
5c 150m, 6c /180m, 7c /210m 8c /240m mc

Where do you see the value before a takeover event ?
If the company was to trade at 2c, is out of the money, so only consider 2b fd = 40m mc., 3c = 60m, but above 3c then its 3b so 3.1c = 93m MC FD.

It comes down to whether the option buyer considers the heads able to value the company at, or its just rabbits buying into expecting the normal tight time premium play .

Yes, you can get a time premium above intrinsic, but you need to be able to then project a value of then say 8c/ 240m, etc onto the target. ie, you only pay that premium id you can justify a forward bet at 8c etc.
Because if someone was to pay say, 1.5c when the heads were at 4c, (a 0.5c premium) then the doubling of the sp, 4c to 8c = 2x and the time premium is justified, so that 1.5c => 5c. = 3.3x

Hence at 4c, and a premium at 1.5c ops, would need a projection of say 8c, to justify a 3.3 V 2 win case on the options.

So its really about what the punter feels the sp target can achieve.