Run same command with different parameters

You can refer to the first word of the previous command line (command in your case) by history expansion !!:0 and then you can just add necessary arguments to it.

command -a && !!:0 -b && !!:0 -c

For example:

% echo foobar && !!:0 spamegg && !!:0 baz    
echo foobar && echo spamegg && echo baz
foobar
spamegg
baz

Note that, as Stéphane Chazelas has pointed out, this can result in unexpected expansions too.

How about a shell function wrapping a loop?

yourcmd() {
    local arg
    for arg; do
        thing "$arg" || return
    done
}

Where "thing" is the actual command you want to invoke. Then simply

yourcmd -a -b -c

You can even generalize this to any command:

splitargs() {
    local cmd arg 
    cmd="$1"
    shift
    for arg; do
        "$cmd" "$arg" || return
    done
}

Then

splitargs somecommand -a -b -c

Amidst the creative and insightful answers, here's something simple in the name of typing fewer characters:

# under the assumption that you have a frequently-used set of flags: -a -b -c
alias c='command -a && command -b && command -c'

# slightly more generally, name some aliases according to the set of flags
alias cabc='command -a && command -b && command -c'
alias cdef='command -d && command -e && command -f'

# more generally, just shorten the command name and then pass whatever flags you want
alias c=command
c -e && c -f && c -f

Make a shell script MultiRun, which takes first Parameter as Command and runs this with remaining Parameters one at a time.

./MultiRun curl A B C D

Your Script should take curl as the command and run "curl A" , "curl B" , "curl C" , "curl D". Now, because your script is in control, you can decide whether a failure in any one command will terminate the script or continue to next Parameter or wait for user input or whatever. You can even decide on the exit status of the whole script, based on the execution of the individual commands.

MultiRun Script can be something like this:

#! /bin/bash
COMMAND=$1
shift #### Remove COMMAND from existing Parameters
for PARAMETER in "$@" ; #### Process all remaining Parameters
do
  $COMMAND $PARAMETER
  # Check exit status and take action or wait for user input , if required
done
# Depending on the individual exit statuses , choose your exit status N with "exit $N"

Now execute this:
./MultiRun echo 1 2 3 4
to get output of "echo 1" , "echo 2" , "echo 3" , "echo 4" like this
1
2
3
4

It is a very flexible & reusable solution.