If I understand correctly, you are submitting expenses to your company in USD, GBP, EUR and then they are using some exchange rate to pay you back in DKK? The only thing you are missing is what exchange rate they are using, right? You could ask them.
If it were me I'd probably do something like this....
2017-11-05 * "Buy coffee"
Assets:Wallet -10 GBP
Expenses:Business
2017-11-05 * "Airfare"
Assets:Credit-Car -2,000 DKK
Expenses:Business
2017-11-05 * "Hotel"
Assets:Credit-Card -500 USD
Expenses:Business
2017-11-05 * "Taxi"
Assets:Wallet -15 EUR
Expenses:Business
2017-11-15 * "Reimbursements"
Income:Reimbursements 3,100 DKK @@ 500 USD
Income:Reimbursements 111 DKK @@ 15 EUR
Income:Reimbursements 84 DKK @@ 10 EUR
Income:Reimbursements 2,000 DKK
Expenses:Business
2017-11-16 balance Expenses:Business 0 USD
2017-11-16 balance Expenses:Business 0 EUR
2017-11-16 balance Expenses:Business 0 GBP
2017-11-16 balance Expenses:Business 0 DKK
After all, if you submitted the expenses one at time, isn't that how you'd enter it? The only complication seems to be the batching of reimbursement and the unknown exchange rate used for calculating the DKK to reimburse?
The more I think about the less I see how exchange rates would come into play...unless you track the exchange rate on the day you acquired the euros in your wallet. I don't think many people do that, even with beancount. The only slippage might be if you pay in USD...which turns into e.g. 1300 DKK on you credit card. But your company only reimburses you a 1250 DKK. But that's just an unreimbursed expense...not FX gain/loss.