Cycle to work scheme

I know it will come down to what my HR say, but as with anything like that. It's best if you just tell them it's allowed ans don't give them an option to say no

I doubt this would fly, it is really up to them how the administer it and whether the second scheme would take them over their self-imposed limits...but to convince them show them para 4.14 of this:

You can hire two cycles to one employee if, for example, a cycle is
used at either end of a train journey between home and place of work

Just don't show them the rest of the para which is from no doubt outdated 2019 guidance but is actually the guidance still linked on the HMRC site