Is it possible to have an afterburner in a turbofan with bypass ratio greater than 1:1?
fooot has pointed out the GE F101 (powers the B-1 Lancer) has a BPR (bypass ratio) of >2:1 and comes with an afterburner.

Other examples are the Turbo-Union RB199 (1.1:1) and the Volvo RM8 (0.97:1). Generally, anything below 4:1 is a low BPR, and bypass air is needed for cooling. Pure turbojets resort to other means of cooling, such as the ram air inlet on a J75, or they run inefficiently at low combustion temperatures.

I can't speak for the inner workings of a classified military engine, but an ideal supersonic engine would be a variable cycle engine (VCE). Operating with bypass in the subsonic regime, and without in the supersonic high-power demand regime.

Such theoretical (to the public at least) examples from the 90's are shown (and linked) below. Do note the idea behind the VCE is the elimination of the wasteful and noisy afterburner.

So, it's an either/or situation. A dual operation of afterburner and high bypass in a non-VCE would not have benefits.

(Flight—PDF) Image shows how a VCE routes the bypass air in both modes of operation. Other variations by RR and Snecma can be seen here. Note the novel design of the Snecma with the free-turbine—extra-fan. VCE's would definitely be heavier and more complex engines.

Related: Why do military turbofan engines use a low bypass ratio?